Theoretical Investigation of the Displacement Burst Observed in Nanoindentation by Collective Dislocation Loops Nucleation Model

Abstract

Abrupt growth of displacement observed in the relationship between indent load and indent depth in nanoindentation of crystalline materials, so-called displacement burst, has been recognized as one of the representative examples of nanoscale plastic behavior (nanoplasticity). This phenomenon corresponds to the early stage of plastic deformation and is greatly influenced by the collective dislocation emission. In the present paper a simplified model is constructed for the first displacement burst with use of the elastic theory based on both the Hertzian contact theory and the classical dislocation theory to evaluate the displacement burst in nanoindentation. The result of the analytical model for the energy equilibrium revealed that there is a strong correlation between burst width and critical indent depth that corresponds to the dislocation emission. Finally, it is shown that more than one hundred high-density dislocations are generated simultaneously and surface step corresponding to the Burgers vector of dislocation dipole of each emitted dislocation causes significant displacement burst.