Evaluation of the thermal phonon emission in dynamic fracture of brittle crystals

We describe in detail how to quantify, computationally, the contribution of the anisotropic and velocity-dependent thermal phonon emission energy release rate during dynamic crack propagation in brittle crystals. The calculations were performed using a procedure based on combined continuum elastodynamics Freund equation of motion and molecular dynamics computer calculations. We used a precracked strip-like specimen subjected to prescribed displacement on the boundaries, commonly used in atomistic calculations of crack dynamics. Various cleavage planes and directions of silicon-like crystal for a wide range of crack speeds were investigated. It is shown that in addition to being strongly dependant on crack speed and atomistic arrangement, the relative phonon emission energy release rate is size dependent, hence governing the size-dependent terminal crack speed. This speed, however, is not influenced by the specimen's initial temperature, ranging between 10K and 300K.