Abstract
Using the lattice Green's function approach, we study the crack/dislocation effects in the fracture both of ductile and brittle (2D) materials. The lattice Green's function for the defective lattice, with dislocation and a crack, are obtained by solving the Dyson equation. The external force, F, with tensile and shear components is applied, as a pair of forces, to the atoms near the center of the crack. In this calculation, the dislocation emission is chosen to be cleavage plane as well as glide plane of the 2D lattice. We compare the cleavage and dislocation emission criteria of the atomistic simulation with those of the linear elasticity theory.
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