Energetics of dislocation nucleation under a nanoindenter

We present an analysis of dislocation nucleation under an idealized nanoindenter based on the variational boundary integral formulation of the Peierls-Nabarro dislocation model. By solving the embryonic dislocation profiles, corresponding to the relative displacements between the two adjacent atomic layers along the slip plane, we have determined the critical conditions for athermal dislocation nucleation as well as the activation energies required to thermally activate embryonic dislocations from their stable to unstable saddle point configurations. The effect of the size of the indenter on the energetics of dislocation nucleation is quantitatively characterized. The result is compared with a simplified analysis based on the application of the Rice model for dislocation nucleation at a crack tip.