Prediction of Micro and Nano Indentation Size Effects from Spherical Indenters

In the present work, a micromechanical model based on dislocation mechanics for predicting indentation size effect from spherical indenters is developed and compared with the most widely used Swadener et al. (2002) model. The key idea proposed here while deriving the model is that a nonlinear coupling between the geometrically necessary dislocations (GNDs) and the statistically necessary dislocations (SSDs) can largely correct the deviation of the Swadener et al. model's prediction from hardness results for small diameter indents. Furthermore, the model can be used in identifying the material length scale from micro- and nano-indentation data.