A precise correcting method for the study of the superhard material using nanoindentation tests
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ao Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Jian Lua) Department of Mechanical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong (Received 20 June 2006; accepted 12 January 2007)
The accurate description of the indentation load–displacement relationship of an elastic sharp indenter indenting into an elastic half-space is critical for analyzing the nanoindentation data of superhard materials using the procedure proposed by Oliver and Pharr [J. Mater. Res. 7, 1564 (1992)]. A further discussion on this issue is made in the present work to reconcile the apparent inconsistencies that have appeared between the experimental results reported by Lim and Chaudhri [Philos. Mag. 83, 3427 (2003)] and the analysis performed by Fischer-Cripps [J. Mater. Res. 18, 1043 (2003)]. It is found that the indenter size effect is responsible for this large discrepancy. Moreover, according to our analysis, we found that when the deformation of the indenter is significant, besides the errors caused by the Sneddon’s boundary condition as addressed by Hay et al. [J. Mater. Res. 14, 2296 (1999)], the errors induced by the application of reduced modulus should be considered at the same time in correcting the modified Sneddon’s solution. In the present work, for the diamond indenter of 70.3° indenting into an elastic half-space with its Poisson’s ratio varying from 0.0 to 0.5 and the ratio of the Young’s modulus of the indented material to that of the diamond indenter, Ematerial/Eindenter, varying from 0 to 1, a set of new correction factors are proposed based on finite element analysis. The results reported here should provide insights into the analysis of the nanoindentation load–displacement data when using a diamond indenter to determine the hardness and Young’s modulus of superhard materials.
I. INTRODUCTION
During the past 3 decades, depth sensing instrumented indentation tests have become an important tool to determine the mechanical properties of materials at different length scales (e.g., nanometer and micrometer scales). Using indentation tests, Young’s modulus and hardness can be measured following the method of Doerner and Nix1 or Oliver and Pharr.2 It is also possible to use indentation tests to determine the stress–strain curves of elastoplastic materials.3–15 Besides being used
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2007.0150 J. Mater. Res., Vol. 22, No. 5, May 2007
on bulk materials, indentation tests can be used to probe the mechanical properties of thin films and coating systems.16,17 The present research is relevant for the analysis of the conical indentation into an elastic half-space, which is useful when taking at least the following two aspects into consideration. First, there indeed exist materials that exhibit elastic deformation under indentation (e.g., rubber-like materials and some superhard materials). Second, the solution of the indentation into an elast
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