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Title: An experimental evaluation of the constant beta relating the contact stiffness to the contact area in nanoindentation

Abstract

Measurements of mechanical properties by nanoindentation with triangular pyramidal indenters like the Berkovich rely heavily upon the relationship between the contact stiffness, S, the contact area, A, and the reduced elastic modulus, E{sub r}. This relationship is often written in the form S=2{beta}E{sub r}(A/{pi}){sup 1/2}, where {beta} is a constant that depends on the geometry of the indenter. Although the most common values for {beta} used in experimental measurements are 1.000 and 1.034, various theoretical analyses have yielded values as small as 1.00 or as large as 1.20, depending on the assumptions made to model the deformation. Here, the most appropriate value of {beta} is explored by performing careful experiments in fused quartz with thin gold coatings applied to the surface to reveal the actual contact area when observed in the scanning electron microscope. Experiments were performed not only with the Berkovich indenter, but with five other three-sided pyramidal indenters with centreline-to-face angles ranging from 35.3{sup o} (cube corner) to 85.0{sup o}. The results are important in the accurate measurement of mechanical properties by nanoindentation.

Authors:
 [1];  [1];  [2];  [3];  [2]
  1. University of Tennessee, Knoxville (UTK)
  2. ORNL
  3. MTS Nanoinstruments Innovation Center, Oak Ridge
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Shared Research Equipment Collaborative Research Center
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
988705
DOE Contract Number:  
DE-AC05-00OR22725
Resource Type:
Journal Article
Journal Name:
Philosophical Magazine A
Additional Journal Information:
Journal Volume: 86; Journal Issue: 33-35; Journal ID: ISSN 1478-6435
Country of Publication:
United States
Language:
English
Subject:
47 OTHER INSTRUMENTATION; 77 NANOSCIENCE AND NANOTECHNOLOGY; NANOSTRUCTURES; COATINGS; FLEXIBILITY; GOLD; MECHANICAL PROPERTIES; QUARTZ; MECHANICAL TESTS; MEASURING INSTRUMENTS; PERFORMANCE TESTING

Citation Formats

Strader, Jeremy H., Shim, Sanghoon, Bei, Hongbin, Oliver, Warren C., and Pharr, George Mathews. An experimental evaluation of the constant beta relating the contact stiffness to the contact area in nanoindentation. United States: N. p., 2006. Web. doi:10.1080/14786430600567747.
Strader, Jeremy H., Shim, Sanghoon, Bei, Hongbin, Oliver, Warren C., & Pharr, George Mathews. An experimental evaluation of the constant beta relating the contact stiffness to the contact area in nanoindentation. United States. doi:10.1080/14786430600567747.
Strader, Jeremy H., Shim, Sanghoon, Bei, Hongbin, Oliver, Warren C., and Pharr, George Mathews. Sun . "An experimental evaluation of the constant beta relating the contact stiffness to the contact area in nanoindentation". United States. doi:10.1080/14786430600567747.
@article{osti_988705,
title = {An experimental evaluation of the constant beta relating the contact stiffness to the contact area in nanoindentation},
author = {Strader, Jeremy H. and Shim, Sanghoon and Bei, Hongbin and Oliver, Warren C. and Pharr, George Mathews},
abstractNote = {Measurements of mechanical properties by nanoindentation with triangular pyramidal indenters like the Berkovich rely heavily upon the relationship between the contact stiffness, S, the contact area, A, and the reduced elastic modulus, E{sub r}. This relationship is often written in the form S=2{beta}E{sub r}(A/{pi}){sup 1/2}, where {beta} is a constant that depends on the geometry of the indenter. Although the most common values for {beta} used in experimental measurements are 1.000 and 1.034, various theoretical analyses have yielded values as small as 1.00 or as large as 1.20, depending on the assumptions made to model the deformation. Here, the most appropriate value of {beta} is explored by performing careful experiments in fused quartz with thin gold coatings applied to the surface to reveal the actual contact area when observed in the scanning electron microscope. Experiments were performed not only with the Berkovich indenter, but with five other three-sided pyramidal indenters with centreline-to-face angles ranging from 35.3{sup o} (cube corner) to 85.0{sup o}. The results are important in the accurate measurement of mechanical properties by nanoindentation.},
doi = {10.1080/14786430600567747},
journal = {Philosophical Magazine A},
issn = {1478-6435},
number = 33-35,
volume = 86,
place = {United States},
year = {2006},
month = {1}
}