Evaluation of the effectiveness of representative methods for determining Young’s modulus and hardness from instrumented indentation data

Abstract

The effectiveness of Oliver & Pharr's (O&P's) method, Cheng & Cheng's (C&C's) method, and a new method developed by our group for estimating Young's modulus and hardness based on instrumented indentation was evaluated for the case of yield stress to reduced Young's modulus ratio (σ[sub y]/E[sub r]) ≥ 4.55 × 10⁻⁴ and hardening coefficient (n) ≤ 0.45. Dimensional theorem and finite element simulations were applied to produce reference results for this purpose. Both O&P's and C&C's methods overestimated the Young's modulus under some conditions, whereas the error can be controlled within ± 16% if the formulation was modified with appropriate correction functions. Similar modification was not introduced to our method for determining Young's modulus, while the maximum error of results was around ± 13%. The errors of hardness values obtained from all the three methods could be even larger and were irreducible with any correction scheme. It is therefore suggested that when hardness values of different materials are concerned, relative comparison of the data obtained from a single standard measurement technique would be more practically useful. It is noted that the ranges of error derived from the analysis could be different if different ranges of material parameters σ[sub y]/E[sub r] and n are considered.