Further investigation on the definition of the representative strain in conical indentation

Further investigation on the definition of the representative strain in conical indentation was performed in this work. In particular, the representative strains proposed in the work of Cao et al. [J. Mater. Res. 20, 1194 (2005)] and Ogasawara et al. [J. Mater. Res. 20, 2225 (2005)] were discussed in detail. For the method using the energy-based representative strain [Cao et al., J. Mater. Res. 20, 1194 (2005)], it is shown that it can be extended to a wider range of material properties (from nearly fully plastic materials to highly elastic materials). For the stress-state-based definition of the representative strain, we found, in contrast with the results reported in the work of Ogasawara et al. [J. Mater. Res. 20, 2225 (2005)], that similar to the constant representative strain reported by Dao et al. [Acta Mater. 49, 3899 (2001)], it works well only for a limited range of engineering materials. Based on this premise, novel definitions of the representative strain, which can lead to a one-to-one relationship with high level of accuracy between the reduced Young's modulus, the indentation loading curvature, and the representative stress are further presented. Detailed numerical analysis performed on nine kinds of engineering materials verified the effectiveness of the proposed representative strains and corresponding dimensionless functions. Experimental verification using the data for the ultrafine crystalline Ni further showed that the results reported in this paper have the potential to be applied in practice.