Construction of CRSS model for sapphire with rate theory and molecular dynamic simulations

Compression test is a popular experiment to study the mechanical behavior of materials during uniaxial loading. In such tests, the critical resolved shear stress (CRSS) is often determined as the characteristic property of material strength. The current work studies CRSS of sapphire under uniaxial compressive stress using molecular dynamic simulations. During each test, a cubic model is subjected to a constant strain rate until plastic deformation is observed, and the CRSS is calculated for each case by applying the Schmid's law. The test is run under various model sizes, strain rates, temperatures, as well as orientations; the CRSS dependencies of these variables are investigated. Furthermore, with the application of rate theory, a mathematical model of CRSS is developed to interpret the variable dependencies. Such a model is fitted to the simulation results to obtain a statistical model. It is found that CRSS of sapphire has a positive relation with strain rate, and negative relations with model size and temperature. For future work, the resulting model can be compared to experimental data, where its effectiveness can be investigated.