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

Abstract

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/σY → 5) to full plastic (E/σY→ 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., Er/σY) 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.

Measurement of the Mechanical Properties of Bone: A Recent History

“…Some have proposed quite complex modifications of the method, mainly relating to the fact that bone is to some extent viscoelastic [46]. Some consider that nanoindentation is actually not well-suited for relatively compliant, anisotropic materials like bone [45]. Nevertheless, I think that this method, or modifications of it, will be important in the future in determining difference in stiffness properties over very small distances.…”

Can Young’s modulus and hardness of wire structural materials be directly measured using nanoindentation?

“…For the bulk materials, the details of the finite element model have been given previously. 14 Because there are no analytical solutions to the problem of conical indentations in elastic-plastic wire structural materials, a 3D finite element model was invoked with the commercial FEM package ABAQUS (HKS Inc., Pawtucket, RI) 15 to systematically investigate the dimensionless functions Eqs. (10) and (11).…”

Effect of Compressive Straining on Nanoindentation Elastic Modulus of Trabecular Bone

“…During the indentation process, the loading rate was set to be 50 μN/s, the holding time was zero, and the unloading rate was set to 50 μN/s. The indentation loaddisplacement data obtained in after nanoindentation tests was analyzed to determine the elastic modulus, E, using the method of Oliver and Pharr, Oliver and Pharr [12,13] and Shu et al [14]. The Poisson's ratio (v t ) and elastic modulus (E t ) of the diamond tip is known to be 0.07 and 1140 GPa, respectively.…”

“…The reasons for such variations include distinct applied strain rates, different representative volume element sizes, and variations in the length scale of the experiments, Hengsberger et al [10]. Nanoscale elastic moduli of bone tissue have been regularly measured using techniques based on the Oliver & Pharr method, Oliver and Pharr [12,13] and Shu et al [14]. Using this method, it is possible to determine the elastic modulus and hardness from indentation load and displacement measurement plots without having the requirement of imaging the impression left by the indenter.…”