Atomistic Study of Fracture of Crystalline Materials by Lattice Green’s Function Method: Effects of Anharmonicity of Lattice Vibration

Abstract

Using the lattice Green’s function approach which includes the temperature dependence of the materials parameters, we study the both cleavage and dislocation emission processes in the fracture of crystalline materials. Firstly, we calculate the Green’s function for the defective lattice, with dislocation and crack, by solving the Dyson equation. After the lattice Green’s functions have been determined, the relaxation problem for the reconstituted bonds in the cohesive zone is solved. The external force F with tensile and shear components is applied, as a pair of forces, to the atoms at the center of the crack. In this lattice Green’s function calculation the temperature effects resulting from the anharmonicity of lattice vibrations are included by introducing the thermal lattice expansion, temperature dependent force constant matrix and temperature dependent non-linear cohesive forces at the crack tip region. We compare the cleavage and dislocation emission processes at the absolute zero temperature with those of the higher temperatures.