Evaluation criteria of the constitutive law formulation for the metal-cutting process

Modelling of the cutting process is necessary to predict cutting forces, residual stresses, and burr formation. A major difficulty in this modelling process is the description of the material behaviour in the primary and the secondary deformation zones, which is characterized by severe plastic deformation at high temperatures and strain rates. The description of the material behaviour requires correct formulation of the constitutive law. Although a number of formulations have been proposed to capture the flow stress behaviour, the assessment of these formulations for the cutting process is still a very difficult task owing to the lack of direct measurements of the high strains, strain rates, and temperatures encountered in the cutting process. This paper presents novel evaluation criteria to assess the degree of accuracy of the constitutive equation under machining conditions. Different existing constitutive laws are identified for Inconel 718, and then evaluated using the proposed criteria. To better describe the plastic behaviour of Inconel 718, new constitutive relationships are formulated and evaluated. From the evaluation results, an accurate description of the constitutive relationship for Inconel 718 is established. This constitutive law is further validated using high-speed split Hopkinson pressure bar (SHPB) tests and orthogonal cutting tests in conjunction with finite element simulations.