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Single crystalline sapphire (-) possesses superior mechanical, thermal, chemical, and optical properties over a wide range of temperatures and pressure conditions, allowing it for a broad spectrum of industrial applications. For the past few decades, research has aimed at comprehensive understanding of its plastic deformation mechanisms under mechanical loading. In this study, we have employed molecular dynamics (MD) simulations to study rhombohedral twinning of sapphire, which is of critical importance in understanding the plastic deformation of sapphire as one of most commonly observed deformation modes. Since the critical resolved shear stress (CRSS) plays a pivotal role in describing the activation of slip systems, it is adopted in this study as the key parameter for analysis. The CRSS is calculated during the uniaxial compression test of a cubic sapphire crystal, oriented to exclusively activate rhombohedral twinning deformation, under simulation conditions such as temperature, strain rate, and system size. Furthermore, a theoretical model of CRSS is constructed based on theories of thermal activation processes, then empirically fitted to CRSS data gathered from the MD simulations. This model accurately captures the relationships between CRSS and external parameters including temperature, strain rate, and system size and shows excellent agreements with the simulation results. 

In this paper, material deformation during ultra-precision machining (UPM) on the C-, R-, and A-planes of sapphire was investigated using the slip/fracture activation model where the likelihood of activation of individual plastic deformation and fracture systems on different crystallographic planes was calculated. The stress data obtained from molecular dynamics (MD) simulations were utilized, and the slip/fracture activation model was developed by incorporating the principal stresses in calculating the plastic deformation and fracture cleavage parameters. The analysis methodology was applied to study material deformation along various cutting orientations in sapphire. The stress field at crack initiation during UPM on C-, R-, and A-planes of sapphire was calculated using molecular dynamics (MD) simulations. An equation describing the relationship between crack initiation and its triggering parameters was formulated considering the systems’ plastic deformation and cleavage fractures. The model can qualitatively predict the crack initiations for various cutting orientations. The proposed model was verified through ultra-precision orthogonal plunge cut experiments along the same cutting orientations as in the MD simulations.