Indentation size effect in metallic materials:: Modeling strength from pop-in to macroscopic hardness using geometrically necessary dislocations

The indentation size effect observed during indentation testing of crystalline materials is modeled in terms of geometrically necessary dislocations using a corrected Nix/Gao model. Considering the size of the plastic zone underneath the indenter, the density of geometrically necessary dislocations is calculated for Berkovich and cube-corner indenters. The statistically stored dislocation density is derived from uniaxial stress-strain data applying the Tabor concept of the representative strain. The depth dependence of hardness is obtained from the Taylor relation, considering the statistically stored and geometrically necessary dislocation densities. Hertzian contact theory is used to describe the elastic deformation of the material, whereas the critical pop-in load is derived from the theoretical strength of the material. The plastic load after pop-in is calculated from the Taylor relation under the assumption of perfect indenter geometry. Good agreement is found for our model approach with indentation data on Ni, Cu, Al, and W for Berkovich and cube-corner indenters at all length scales. The indentation response of pure metals can thus be modeled from pop-in to macroscopic hardness using uniaxial stress-strain data. (c) 2006 Published by Elsevier Ltd on behalf of Acta Materialia Inc.