It was noted that the homogeneous nucleation of a dislocation beneath a nano-indenter was a strain-localization event which was triggered by elastic instability of a perfect crystal at finite strains. Finite-element calculations, using a hyperelastic constitutive relationship that was based upon an interatomic potential, was exploited as being an efficient method for characterizing this instability. This facilitated the study of dislocation nucleation at length scales that were large when compared to atomic dimensions; yet maintained non-linear interatomic interactions. An instability criterion, based upon bifurcation analysis, was incorporated into the finite-element calculation in order to predict homogeneous dislocation nucleation. This criterion was superior, to one based upon the critical resolved shear stress, in terms of its accuracy in predicting the nucleation site and the slip nature of the defect. Finite-element calculations of the nano-indentation of a single crystal, by a cylindrical indenter, and predictions of dislocation nucleation were checked by comparison with direct molecular dynamics simulations which were governed by the same interatomic potential. Analytical 2-dimensional and 3-dimensional linear elastic solutions, based upon the Stroh formalism, were used to bench-mark the finite-element results. The critical configuration for homogeneous dislocation nucleation beneath a spherical indenter was quantified by means of full 3-dimensional finite-element calculations. The predicted nucleation site and slip nature were checked by direct molecular dynamics simulation. The critical stress state at the nucleation site, as deduced from the interatomic potential, was in quantitative agreement with first-principles density functional theory calculation.

Predictive Modeling of Nano-Indentation Induced Homogeneous Dislocation Nucleation in Copper. T.Zhu, J.Li, K.J.Van Vliet, S.Ogata, S.Yip, S.Suresh: Journal of the Mechanics and Physics of Solids, 2004, 52[3], 691-724