Predicting the Shear Plane Angle in Machining From Workmaterial Strain-Hardening Characteristics

Abstract

An upper-bound type analysis is presented for predicting the “shear plane angle,” φ, in machining, using workmaterial strain-hardening characteristics. The degree of strain-hardening is quantified by referring to standard reference tables for yield strength and ultimate strength. In the model, the first step is to formulate the lowest amount of plastic work needed to cause a shear instability (collapse) in severely strain-hardened material. (In an upper-bound analysis this occurs on a plane at (φ = 45 + α/2.) However, due to work-hardening, this deformation zone geometry is nonunique and the shear plane can “rotate” into the softer material ahead of this initial instability. Using the proposition that the plastic work input remains constant, an equation is then derived which can be used to calculate the degree of shear plane rotation and hence the final position that the shear plane adopts for various workmaterials. In discussion, it is emphasized that this is an introductory analysis which ignores friction at the rake face and the high strain rates and temperatures that arise in practice; however, the agreement between this new, predictive model and experimental data is exceptionally good.