Crystallographic Orientation and Tool Geometry Coupled Model for Brittle-Ductile Transition Prediction

Abstract The brittle–ductile transition depth is a key parameter for understanding material removal mechanisms and achieving damage-free surfaces in the machining of brittle single crystals. However, existing predictive models often neglect crystallographic anisotropy and the scale-dependent effects associated with the tool edge radius in micro-cutting. To address these limitations, a multi-parameter anisotropic model is developed to predict the critical depth-of-cut, incorporating directional variations in hardness, elastic modulus, shear modulus, fracture toughness, and specific surface energy. Edge-radius-related corrections are introduced into the effective rake and shear angles to account for the local stress fields present in micro-cutting. The model is validated through multi-directional scratch tests on CaF2, single-crystal Si, and single-crystal Ge. On the Ge (1 0 0) plane, the predicted maximum and minimum critical depths differ from experimental results by only 2 nm, representing a 60% improvement compared with models that ignore edge-radius effects. Additional experiments show that larger tool nose radii produce higher critical depths-of-cut, and this trend is accurately reproduced by the model.