**Mesoscale Analysis of Homogeneous Dislocation Nucleation**

A Garg and A Hasan and CE Maloney, JOURNAL OF APPLIED MECHANICS- TRANSACTIONS OF THE ASME, 86, 091005 (2019).

DOI: 10.1115/1.4043885

We perform atomistic simulations of dislocation nucleation in two-
dimensional (2D) and three-dimensional (3D) defect-free hexagonal
crystals during nanoindentation with circular (2D) or spherical (3D)
indenters. The incipient embryo structure in the critical eigenmode of
the mesoregions is analyzed to study homogeneous dislocation nucleation.
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. The lowest energy eigenmode for
mesoregions of varying radius, r(meso), centered on the localized region
of the critical eigenmode is computed. The energy of the lowest
eigenmode, lambda(meso), decays very rapidly with increasing rmeso and
lambda(meso) approximate to 0 for r(meso) greater than or similar to xi.
The analysis of a mesoscale region in the material can reveal the
presence of incipient instability even for r(meso) less than or similar
to xi but gives reasonable estimate for the energy and spatial extent of
the critical mode only for r(meso) greater than or similar to xi. When
the mesoregion is not centered at the localized region, we show that the
mesoregion should contain a critical part of the embryo (and not only
the center of embryo) to reveal instability. This scenario indicates
that homogeneous dislocation nucleation is a quasilocal phenomenon.
Also, the critical eigenmode for the mesoscale region reveals
instability much sooner than the full system eigenmode. We use mesoscale
analysis to verify the scaling laws shown previously by Garg and Maloney
in 2D **2016, "Universal Scaling Laws for Homogeneous Dissociation
Nucleation During Nano-Indentation," J. Mech. Phys. Solids, 95, pp.
742-754.** for the size, xi, and depth from the surface, Y*, of the
dislocation embryo with respect to indenter radius, R, in full 3D
simulations.

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