Dynamic hardness and reduced modulus determination on the (001) face of beta-Sn single crystals by a depth sensing indentation technique

Sahin O., Uzun O., Kolemen U., Ucar N.

JOURNAL OF PHYSICS-CONDENSED MATTER, vol.19, no.30, 2007 (SCI-Expanded) identifier identifier


In this work, the creep behaviour of beta-Sn single crystals having different growth directions under different peak indentation test loads (10, 20, 30, 40, and 50 mN) was investigated at room temperature during indentation tests. It was found that a 'nose' appears in the unloading segment of the applied indentation test load penetration depth curve. When a 'nose' occurs, the apparent unloading stiffness Su, defined as dP/dh, is negative and the reduced modulus can no longer be calculated from the Oliver-Pharr method (Oliver and Pharr 1992 J. Mater. Res. 7 1564). The 'nose' disappears when the load hold before unload is lengthened. The correction term due to the creep is the ratio of indenter displacement rate at the end of the load hold to unloading rate (Feng and Ngan 2002 J. Mater. Res. 17 660; Tang and Ngan 2003 J. Mater. Res. 18 1141). Besides, the effect of creep on contact-depth measurement is considered. Removal of creep effects in both contact-area and contact stiffness measurement leads to satisfactory prediction of the dynamic hardness (Hd) and reduced modulus in beta-Sn single crystals. The experimental results reveal that the measured hardness values exhibit a peak-load dependence, i.e. an indentation size effect (ISE). Such peak-load dependence is then analysed using the Meyer law, the Hays-Kendall approach, the proportional specimen resistance (PSR) model, the modified PSR (MPSR) model, and the Nix-Gao model. As a result, the modified PSR model is found to be the most effective one for Hd determination of beta-Sn single crystals.