Novel approach to characterize the deformation under Berkovich and spherical indentations: Study on magnesium single crystals

In this work, we have developed a mathematical framework to investigate the deformation response under Berkovich and spherical indenters. Nanoindentation experiments are carried out on two single-crystal magnesium (Mg) samples oriented for basal slip and tensile twinning. The indentation load vs penetration depth curves are then analyzed to explain the pop-in events with the help of Schmid factor analysis and to identify the favorable deformation modes directly beneath and around the indentation. These results explain why there is only a small difference in the values of hardness between the two orientations despite having a significant difference in their crystallographic orientations. In addition to this, the role of indenter tip radius on the formation of extension twins when indented along the crystallographic $c$ axis is analyzed with the help of a simple analytical model.