Predictive modeling of transition undeformed chip thickness in ductile-regime micro-machining of single crystal brittle materials

This paper proposes a predictive model to determine the undeformed chip thickness in micro-machining of single crystal brittle materials, where the mode of chip formation transitions from the ductile to the brittle regime. The comprehensive model includes a force model considering the rounded tool edge radius effect and ploughing. Irwin's model for computing the stress intensity factor is adopted here as it gives a relation between the stress intensity and applied normal stress including effects of crack size and crack inclination. The occurrence of plastic deformation is built upon the condition that the shear stress in the chip formation region must be greater than the critical shear stress for chip formation and the stress intensity factor must be less than the fracture toughness of the material. The point of transition takes place when the fracture toughness is equal to the stress intensity factor. The above conditions form the theoretical basis for the proposed model in determining the transition undeformed chip thickness. End-turning experiments have been conducted using a single crystal diamond cutting tool on (1 1 1) single crystal silicon, and the results compared to the model predictions for validation. The proposed model would support the determination of the cutting conditions for the micro-machining of a brittle material in ductile manner without resorting to trial and error.