A nano-indentation model for spherical indenters

A model is developed for nano-indentation with spherical indenters. It is based on the Taylor dislocation model and is an extension of Qu et al's (2006 Int. J. Plast. 22 1265-86) micro-indentation model for spherical indenters to nano-indentation. For relatively large indenters (e.g. radii on the order of 100 νm), the present model degenerates to Qu et al (2006 Int. J. Plast. 22 1265-86). For small indenters (e.g. radii on the order of 10 νm), the maximum allowable geometrically necessary dislocation (GND) density is introduced to cap the GND density such that the latter does not become unrealistically high for small indenters. The present nano-indentation model agrees well with the indentation hardness data of iridium for both nano-and micro-indentation.