Indenter tip radius effect on the Nix-Gao relation in micro- and nanoindentation hardness experiments

Nix and Gao established an important relation between microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments (indentation depths in the micrometer range , but it does not always hold in nanoindentation experiments (indentation depths approaching the nanometer range). We have developed a unified computational model for both micro- and nanoindentation in an effort to understand the breakdown of the Nix-Gao relation at indentation depths approaching the nanometer scale. The unified computational model for indentation accounts for various indenter shapes, including a sharp, conical indenter, a spherical indenter, and a conical indenter with a spherical tip. It is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The unified computational model for indentation indeed shows that the Nix-Gao relation holds in microindentation with a sharp indenter, bur it does not hold in nanoindentation due to the indenter tip radius effect.