Molecular dynamics — simulations of the fracture toughness of sapphire

A new method for the estimation of the fracture toughness KIC by using the Molecular Dynamics method is presented. The Al2O3 single crystals were deformed under constant displacement conditions with an initial crack of length 1 nm. The strain was applied in the a axis, which was set perpendicular to the crack plane, so that the mode I crack deformation was achieved. The total energy, which is a result of MD simulations, was analyzed in the elastic, plastic and surface energy part. From the structural plots the crack propagation was measured and the analysis using the Griffith criterion was applied. From the critical condition the fracture toughness was estimated. The experimental values for the fracture toughness in the four crack orientations (plane and direction) (11.0)[001], (11.-2)[12-1], (00.1)[100], and (11.0)[010] were 2.84, 2.71, 5.62, 2.67 MPa m−1/2, respectively, and the calculations are in good agreement. Also, a heterogeneous alumina–zirconia nanocomposite material was analyzed by this method. Although the particle had only a diameter of 1 nm, the toughness increased because the interface was found to be quite strong.