Universal scaling laws for homogeneous dislocation nucleation during nano-indentation

We perform atomistic simulations to study the mechanism of homogeneous dislocation nucleation in two dimensional (2D) hexagonal crystals during nanoindentation with a circular indenter of radius R. We study both a realistic embedded atom method (EAM) potential for Al in addition to simple pair-wise potentials: Lennard-Jones, Morse, and Hookean springs. The nucleation process is governed by the vanishing of the energy associated with a single energy eigenmode. The critical eigenmode, or dislocation embryo, is found to be localized along a line (or plane in 3D) of atoms with a lateral extent, xi, at some depth, Y*, below the surface. For all interatomic potentials, the scaled critical load, F-c/R, and scaled critical contact length, C-c/R, decrease to R-independent values in the limit of large R. However, xi/R and Y*/R display non-trivial scaling with R despite the R independence of F-c/R and C-c/R. We show that although both the interaction potential and the orientation of the lattice affect the prefactors in the scaling relations, all the scaling laws are robust. Furthermore, we show that a stability criterion proposed by Van Vliet et al. based on the minimum eigenvalue, A, of the local acoustic tensor predicts the location, orientation, and polarization of the dislocation embryo with a high degree of accuracy for all potentials and crystallographic orientations. However, we also show that, for all crystallographic orientations and interaction potentials, A erroneously indicates instability before the true instability occurs. (C) 2016 Elsevier Ltd. All rights reserved.