Quantifying the early stages of plasticity through nanoscale experiments and simulations

Nucleation and kinetics of defects at the atomic scale provide the most fundamental information about the mechanical response of materials and surfaces. Recent advances in experimental and computational analyses allow us to study this phenomenon in the context of nanoindentation and localized mechanical probing of surfaces. Here, we present an analytical formulation of the elastic limit that predicts the location and slip character of a homogeneously nucleated defect in crystalline metals, and extend this formulation to the atomic scale in the form of an energy-based, local elastic stability criterion, termed the $\Lambda$ criterion. We demonstrate that this approach can be incorporated efficiently into computational methods such as molecular dynamics and finite-element models. Furthermore, we validate and calibrate the $\Lambda$ criterion directly through nanoindentation experiments and two-dimensional experimental analogs such as the bubble raft model. We outline explicitly a compact and efficient application of the $\Lambda$ criterion within the context of a nonlinear, interatomic potential finite-element model (IPFEM). Further, we report three-dimensional molecular dynamics simulations in several face-centered cubic systems that elucidate the transition from the initiation to the early stages of plasticity during nanoindentation of metals, as characterized by homogeneous and heterogeneous nucleation of up to hundreds of dislocations. Correlation of these simulations with direct observations from nanoindentation experiments provides atomistic insights into the early stages of plasticity.