On the determination of reduced Young's modulus and hardness of elastoplastic materials using a single sharp indenter

In this work, we analyzed the theoretical errors of reduced Young's modulus and hardness of materials provided by single sharp indenter algorithms. According to the analysis, two conclusions can be drawn. First, various methods that use only the indentation loading and unloading curves from a single sharp indenter and omit the effect of the strain hardening exponent own the same widths of the theoretical error bands defined here. They are WE_b for reduced Young's modulus and WH_b for hardness. Second, the upper-bounds, B_E^U and B_H^U, and lower-bounds, B_E^L and B_H^L, of theoretical errors of the measured reduced Young's modulus and hardness might be different for different methods. These conclusions, on the one hand, are relevant to the evaluation of various established single sharp indenter algorithms. On the other hand, they provide useful information (i.e., to optimize the theoretical error bounds) for correcting an established method and the development of new single sharp indenter algorithms. According to the conclusions, an energy-based method has been devised to determine reduced Young's modulus and hardness of materials from nanoindentation tests using a standard Berkovich or Vickers indenter (equivalent to a 70.3° cone). It has been shown that the present method owns the reasonable theoretical error bounds and can provide stable results in the presence of data errors.