A systematic study of the validation of Oliver and Pharr’s method

Oliver and Pharr’s method (O&P’s method) is an efficient and popular way of measuring the hardness and Young’s modulus of many classes of solid materials. However, there exists a range of errors between the real values and the calculated values when O&P’s method is applied to materials not included in the basic assumption proposed initially. In this article, the dimensional analysis theorem and the finite element method are applied to evaluate errors for high elastic (E/σ_Y→ 5) to full plastic (E/σ_Y_{}→ 1000) materials with different strain-hardening exponents from 0 to 0.5. A new method is proposed to correct errors obtained using O&P’s method. The numerical simulation results show that the errors obtained using O&P’s method, given in the form of charts, are mainly dependent on the ratio of the reduced Young’s modulus to the yield stress (i.e.,E_r/σ_Y) and the strain-hardening exponent,n, for an indenter with a fixed included angle. The two mechanical properties, which can be extracted from the load–depth curves of two indenters with different included angles, are used to correct the errors in the hardness and Young’s modulus of the indented materials produced by O&P’s method.