Nonlocal instability analysis of FCC bulk and (1 0 0) surfaces under uniaxial stretching

The objective of this paper is to examine the instability characteristics of both a bulk FCC crystal and a (1 0 0) surface of an FCC crystal under uniaxial stretching along a 〈1 0 0〉 direction using an atomistic-based nonlocal instability criterion. By comparison to benchmark atomistic simulations, we demonstrate that for both the FCC bulk and (1 0 0) surface, about 5000–10,000 atoms are required in order to obtain an accurate converged value for the instability strain and a converged instability mode. The instability modes are fundamentally different at the surface as compared to the bulk, but in both cases a strong dependence of the instability mode on the number of atoms that are allowed to participate in the instability process is observed. In addition, the nonlocal instability criterion enables us to determine the total number of atoms, and thus the total volume occupied by these atoms, that participate in the defect nucleation process for both cases. We find that this defect participation volume converges as the number of atoms increases for both the bulk and surface, and that the defect participation volume of the surface is smaller than that of the bulk. Overall, the present results demonstrate both the necessity and utility of nonlocal instability criteria in predicting instability and subsequent failure of both bulk and surface-dominated nanomaterials.