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Effective Poisson’s ratio from combined normal and lateral contacts of single crystals

Published online by Cambridge University Press:  26 October 2011

J.H. Lee ,
Y.F. Gao  and
G.M. Pharr
J.H. Lee*
Affiliation:
Division for Research Reactor, Korea Atomic Energy Research Institute, Daejeon 305-353, Republic of Korea
Y.F. Gao*
Affiliation:
Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996; and Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
G.M. Pharr
Affiliation:
Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996; and Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
*
a)Address all correspondence to these authors. e-mail: [email protected]
b)e-mail: [email protected]
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Abstract

When an elastic half-space is subjected to both normal and tangential contact, the ratio of normal and tangential contact stiffnesses can be measured by various scanning force microscopy techniques. For elastically isotropic solids, this stiffness ratio depends on Poisson’s ratio as given by the Mindlin solution. An anisotropic elastic contact analysis here shows the difference between the effective Poisson’s ratio as defined from the stiffness ratio and its uniaxial counterpart with respect to various crystal structures and various normal/tangential contact directions. Closed-form analytical solutions of effective indentation moduli are derived for materials with at least one plane of transverse isotropy. Since the Sneddon (normal contact) and Mindlin (lateral contact) solutions are derived under different frictional conditions, finite element simulations were performed which show that the effects of elastic dissimilarity and contact shape are generally small but not negligible. The predicted dependence on crystallographic orientation and elastic anisotropy has been compared favorably with previously reported multiaxial contact experiments for a number of cubic single crystals. Implications for atomic force microscopy based experiments are also discussed.

Keywords

NanoindentationElastic properties
Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 1: Focus Issue: Instrumented Indentation , 14 January 2012 , pp. 182 - 191
Copyright
Copyright © Materials Research Society 2011

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References

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