A single vacancy as a stress concentrator in a planar crystal subjected to tensile loading: A discrete analog of the Kirsch problem

The effect of a single fixed vacancy on the stress concentration factor and fracture of a 2D crystal is investigated numerically applying a molecular statics technique. The results show that the stress concentration factor is crystal size- and strain-dependent, and that there is such size that at small strains this factor is equal to 3, which is the value near the hole in a plate according to the classical Kirsch problem. The stress–strain curves exhibit nonlinear elasticity and the fracture can be characterized as brittle since no dislocations have been developed during the loading. The results raise the question of how to define a representative crystal size which can adequately represent continuum in a multi-scale modeling.