Technical Briefs

A Comparison of Coulomb Friction and Friction Stress Models Based on Multidimensional Nanocontact Experiments

[+] Author and Article Information
Y. F. Gao1

Department of Materials Science and Engineering,  University of Tennessee, Knoxville, TN 37996ygao7@utk.edu

H. T. Xu, G. M. Pharr

Department of Materials Science and Engineering,  University of Tennessee, Knoxville, TN 37996

W. C. Oliver

Nano Instrument Innovation Center,  MTS System Corporation, Oak Ridge, TN 37830


Corresponding author.

J. Appl. Mech 75(3), 034504 (May 05, 2008) (3 pages) doi:10.1115/1.2871022 History: Received April 17, 2007; Revised December 18, 2007; Published May 05, 2008

The accuracy of the Oliver–Pharr approach for nanoindentation experiments critically depends on the interfacial friction condition. Although Coulomb friction is often used in finite element simulations for the correction, the friction stress model may give a more appropriate physical scenario. The measurement of the tangential contact stiffness by a recently developed multidimensional nanocontact system provides a direct verification of these two friction models. Both friction models will predict the tangential stiffness reduction as the consequence of interface microslip, but quantitative comparison to the experiments supports the friction stress model.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

(a) Geometric conventions used in the axisymmetric contact problem. The contact radius is a and the stick zone radius is c. The slip zone is assumed to be annular. (b) The ratio of measured tangential to normal contact stiffness is plotted against the penetration depth of a Berkovich diamond indenter into the surface of bulk aluminum single crystal and fused silica (original data from Dr. B. N. Lucas). Data at large indentation depths agree with the elastic contact prediction, and the transient region at small indentation depths will be used to evaluate the interfacial friction condition.

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Figure 2

Stiffness measurements of aluminum single crystal are compared to the predictions by the two friction models. Least squares fittings give rise to acrtcohesive=192nm for the friction stress model in (a), and acrtCoulomb=118nm for the Coulomb friction model in (b). The straight and curved solid lines correspond to stiffness ratio at δx=0 and δx=δmax, respectively. The two dashed lines are computed from the uniform weighted average (top curve, blue color online) and biased weighted average (bottom curve, magenta color online). The friction stress model leads to better agreement with the experiments.



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