Fundamental relations used in nanoindentation: Critical examination based on experimental measurements
- PDF / 140,983 Bytes
- 8 Pages / 612 x 792 pts (letter) Page_size
- 64 Downloads / 236 Views
he fundamental relations used in the analysis of nanoindentation load–displacement data to determine elastic modulus and hardness are based on Sneddon’s solution for indentation of an elastic half-space by rigid axisymmetric indenters. It has been recently emphasized that several features that have important implications for nanoindentation measurements are generally ignored. The first one concerns the measurement of the contact depth, which is actually determined by using a constant value ⑀ ⳱ 0.75 for the geometry of a Berkovich indenter and for any kind of material, whereas the reality is that ⑀ is a function of the power law exponent deduced from the analysis of the unloading curve. The second feature concerns the relation between contact stiffness, elastic modulus, and contact area, in which a correction factor ␥ larger than unity is usually ignored leading to a systematic overestimation of the area function and thus to errors in the measured hardness and modulus. Experimental measurements on fused quartz are presented that show the variation of ⑀ with the geometry of the tip–sample contact; that is to say with the contact depth, as well as the existence of the correction factor ␥, as predicted in some recent articles. Effects of both ⑀ and ␥ on harness and modulus measurements are also shown.
I. INTRODUCTION
In the past two decades, a great deal of effort has been directed toward the development of techniques for characterizing the mechanical properties of thin films and small volumes of material. Nanoindentation is one means by which this has been achieved.1 One of the more commonly used methods for analyzing nanoindentation load– displacement data is that of Oliver and Pharr,2 which expands on earlier ideas developed by Loubet et al.3 and Doerner and Nix.4 In the Oliver and Pharr (O&P) method, the hardness H and the reduced modulus Er are derived from Pmax , (1) H= A and S=
2
公
Er
公A
,
(2)
where Pmax is the maximum indentation load, A is the projected contact area, and S the unloading stiffness measured at the maximum depth of penetration hmax. A a)
Address all correspondence to this author. e-mail: [email protected] J. Mater. Res., Vol. 17, No. 9, Sep 2002
http://journals.cambridge.org
Downloaded: 12 Mar 2015
reduced modulus is used in the analysis to account for the fact that elastic deformation occurs in both the indenter and the specimen, given by
冋
1 − 2 1 − 21 Er = + E Ei
册
−1
(3)
,
where E, E i , and , i are Young’s modulus and Poisson’s ratio of the specimen and indenter, respectively. In the O&P approach, the projected area A corresponding to the projected area of the elastic contact is considered to be equal to the residual plastic deformation, which is derived by evaluating an empirically determined indenter shape function at the contact depth hc, that is, A ⳱ f(hc). The functional form of f(hc) must be established prior to analysis, by using a calibration procedure that takes into account the load frame compliance and allows calculation of the indenter geometry by
Data Loading...
