The cylindrical nano-indentation on metal film/elastic substrate was studied using two-dimensional discrete dislocation plasticity combined with commercial software, with a focus on the storage volume for geometrically necessary dislocations inside the films and the nano-indentation size effect. The calculations showed that almost all geometrically necessary dislocations were stored within a rectangular area determined by the film thickness and the actual contact width. The variations of indentation contact width with indentation depth for various film thicknesses and indenter radii were fitted by an exponential relation, and then the geometrically necessary dislocation density underneath the indenter was estimated. Based on the Taylor dislocation model and Tabor formula, a simple model for the dependence of the nano-indentation hardness of the film/substrate system on the indentation depth, the indenter radius and the film thickness was established, showing a good agreement with the present numerical results.

Cylindrical Nano-Indentation on Metal Film/Elastic Substrate System with Discrete Dislocation Plasticity Analysis: a Simple Model for Nano-Indentation Size Effect. C.Ouyang, Z.Li, M.Huang, H.Fan: International Journal of Solids and Structures, 2010, 47[22-23], 3103-14