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Research Papers

A Two-Parameter Function for Nanoscale Indentation Measurement of Near Surface Properties

[+] Author and Article Information
K. Farhang

Department of Mechanical Engineering and Energy Processes, Southern Illinois University Carbondale, Carbondale, IL 62901farhang@siu.edu

L. E. Seitzman, B. Feng

 Advance Material Technology, Surface Engineering and Tribology, Caterpillar Inc., Mossville, IL 61525

J. Tribol 130(1), 011005 (Dec 06, 2007) (6 pages) doi:10.1115/1.2805436 History: Received May 02, 2006; Revised March 29, 2007; Published December 06, 2007

A two-parameter function for estimation of projected area in instrumented indentation measurement is obtained to account for indenter tip imperfection. Imperfection near indenter tip is modeled using a spherical function and combined with a linear function describing the edge boundary of the indenter. Through an analytical fusion technique, the spherical and linear functions are combined into a single function with two unknown geometric parameters of tip radius of curvature and edge slope. Data from indentation measurement of force and displacement, using a Berkovich tip and single crystal alumina and silica samples, are implemented in the proposed area function yielding estimated values of Young’s modulus. Results were compared with that obtained from Oliver and Pharr technique for deep as well as shallow indentation regimes. The estimates for Young’s modulus were found to agree quite favorably. More importantly, in contrast to the Oliver–Pharr technique, the use of the two-parameter function resulted in a significantly more accurate estimation of Young’s modulus for shallow indentation depth of 050nm. The error in estimation of Young’s modulus was found to be within 10% for indentation depths of 2550nm and within 20% for indentation depths of 025nm.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Berkovich indenter geometry and its coordinate system

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Figure 2

SEM image of a Berkovich tip showing submicron features

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Figure 3

Indenter profile

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Figure 4

Approximation of indenter tip’s circular profile

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Figure 5

Exact and approximate indenter profiles and the percent error

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Figure 6

An example of load sequence in indentation measurement (data provided by NIST)

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Figure 7

Load-displacement history corresponding to the load sequence in Fig. 6 (courtesy of NIST)

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Figure 8

Comparison of various methods for corrected depth range of 0–200nm; note that the curve by Oliver–Pharr method is out of the window shown, see Fig. 9

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Figure 9

Comparison of various methods for corrected depth range of 0–1800nm

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Figure 10

Area functions: measured and predicted

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Figure 11

Area functions: measured and predicted—shallow indentation range

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Figure 12

Estimated modulus in GPa and estimation error

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