The effect of work-hardening and pile-up on nanoindentation measurements

Nanoindentation is performed on the cross-section of copper samples subjected to surface mechanical attrition treatment (SMAT). The cross-section of the SMAT samples provides a unique microstructure with varying amounts of work-hardening depending on the distance from the SMAT surface. Results show that for a given indentation load the pile-up height decreases and the indentation depth increases as the distance from the SMAT surface increases, both following a power law relationship. Based on image analysis of the indented surface this increase in the pile-up height and decrease in indentation depth is attributed to the localization of plastic strain due to the increased resistance to dislocation motion in the work-hardened region. For a given amount of work-hardening (in terms of distance from SMAT surface), the indentation depth increased with the indentation load obeying a power law relationship with the exponent ranging from 0.58 to 0.68. However, the pile-up height increased linearly with the load, with the rate (slope) increasing with the amount of work-hardening. The observed linear increase in pile-up height with indentation load would naturally introduce an indentation size effect (ISE) if the hardness is corrected for the pile-up. Interestingly, this ISE associated with pile-up increased with an increase in indentation depth, in contradiction to the ISE associated with strain gradient. Deviation of the hardness values corrected for pile-up from the bulk behavior due to surface effect is highlighted and a method to obtain a bulk-equivalent hardness quantity representing the bulk behavior is proposed.