Extension of Oxley’s Analysis of Machining to Use Different Material Models

The aim of the present work is to extend the applicability of Oxley's analysis of machining to a broader class of materials beyond the carbon steels used by Oxley and co-workers. The Johnson-Cook material model, history dependent power law material model and the Mechanical Threshold Stress (MTS) model are used to represent the mechanical properties of the material being machined as a function of strain, strain rate and temperature. A few changes are introduced into Oxley's analysis to improve the consistency between the various assumptions. A new approach has been introduced to calculate the pressure variation along the alpha slip lines in the primary shear zone including the effects of both the strain gradient and the thermal gradient along the beta lines. This approach also has the added advantage of ensuring force equilibrium of the primary shear zone in a macroscopic sense. The temperature at the middle of the primary shear zone is calculated by integrating the plastic work thereby eliminating the unknown constant η. Rather than calculating the shear force from the material properties corresponding to the strain, strain rate and temperature of the material at the middle of the shear zone, the shear force is calculated in a consistent manner using the energy dissipated in the primary shear zone. The thickness of the primary and secondary shear zones, the heat partition at the primary shear zone, the temperature distribution along the tool-chip interface and the shear plane angle are all calculated using Oxley's original approach. The only constant used to fine tune the model is the ratio of the average temperature to the maximum temperature at the tool-chip interface (ψ). The performance of the model has been studied by comparing its predictions with experimental data for 1020 and 1045 steels, for aluminum alloys 2024-T3, 6061-T6 and 6082-T6, and for copper. It is found that the model accurately reproduces the dependence of the cutting forces and chip thickness as a function of undeformed chip thickness and cutting speed and accurately estimates the temperature in the primary and secondary shear zones.

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