A unified approach to quantify the material and geometrical effects in indentation size effect

The seminal work of Nix and Gao in (J Mech Phys Solids, 46:411–425, 1998), laid the foundation for quantifying indentation size effect (ISE). Several groups around the world have continued to explore the various factors that influence ISE, through extensive numerical and experimental studies. In this work, a unified approach to quantify ISE is presented, wherein the effects of materials, geometry and other coupled parameters on ISE are incorporated to derive a simple unified model. The model predictions for depth dependence of hardness are validated through experimental studies on pulsed electro-deposited (PED) nickel with varying grain sizes using a Berkovich tip with a finite tip radius. Lower grain sizes, higher statistically stored dislocation densities, blunt tips, lower constraint factors and higher plastic zone sizes are found to reduce ISE. The deviation caused by these parameters from the predictions of the original Nix & Gao model are discussed. Graphical abstract: [Figure not available: see fulltext.].