On the measurement of pile-up corrected hardness based on the early Hertzian loading analysis

Nanoindentation has been used to gain insight into the elastic/plastic contact responses of material at very small scales. The Oliver and Pharr's analysis (W.C. Oliver and G.M. Pharr, J. Mater. Res. 7 (1992) 1564) on the nanoindentation curve, however, can be meaningless when plastically deformed material piles around the indented points. This study suggests a measuring methodology of the real contact area enlarged by the material pile-up and its corresponding mechanical properties; the pile-up corrected contact area can be calculated inversely from the reduced modulus formulation with input information of the independently determined Young's modulus based on the Hertzian loading analysis. This contact correction relaxed overestimates in the elastic modulus and hardness interpreted from the nanoindentation curve and yielded actual mechanical properties comparable to the literature values of a (100) tungsten monocrystal. In addition, theoretically estimated upheaval amount of the contact boundary in this study was nearly consistent with the average pile-up height measured from an atomic-force microscope.