Mechanics of the Metal Cutting Process. II. Plasticity Conditions in Orthogonal Cutting

The analysis of the mechanics of orthogonal cutting with a type 2 chip as presented in the first paper of this series can be extended by introducing those physical properties of the work material which control its plastic behavior. One evident plasticity condition is the equality of the shear stress on the plane of shear to the shear strength of the metal. If it is also assumed that the shear strength of the work material is a constant and is the only quantity controlling its plastic behavior, then a very simple additional plasticity condition is obtained by application of the principle of minimum energy. This condition is 2φ+τ−α=90°, where φ is the shear angle, τ the friction angle, and α the rake angle. This condition, however, is found by experiment to be a poor approximation in the case of polycrystalline metals. A very good approximation is obtained, though, if use is made of the fact that the shear strength of the polycrystalline metal is actually a function of the compressive stress on the shear plane. The resulting plasticity condition is cot (2φ+τ−α)=k, where k is the slope of the linear curve relating shear strength and compressive stress, and is thus a constant of the work material. Such a plasticity condition establishes a relationship between the force system and the geometry of chip formation, so that, if k and the shear strength be known for a given material, all forces involved in cutting it can be calculated with reasonably good accuracy directly from measurements of chip geometry only, without use of a tool dynamometer. This is of importance in the analysis of practical machining operations.