Hertz Elastic Contact in Spherical Nanoindentation Considering Infinitesimal Deformation of Indenter

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Many studies have been performed to identify and analyze unusual nano-scale phenomena. Violation of Hertz elastic contact between the spherical nanoindenter and metallic materials has been discussed in previous studies. The unexpected results obtained using a spherical indenter raised doubts about elastic contact in nanoindentation. We performed fully elastic loading and unloading nanoindentation on fused silica. To characterize the actual geometry of spherical indenter we directly measured indenter geometry with an atomic-force microscope. We confirmed the actual indenter radius in the experiments by comparison to indenter radius measured by residual impression size above 200 nm indentation depth. The Hertz equation was found to underestimate the indentation depth. To understand this phenomenon, we reconsidered the frame compliance, which is taken as constant in general nanoindentation testing. The infinitesimal deformation of the spherical indenter was calculated by summing the partial compliances of the infinite cylinder of the indenter. We found that indenter compliance depends on indentation depth on a logarithmic scale. We adopted indentation-depth-dependent frame compliance to evaluate accurate load and depth data for indentation depth less than 100 nm. The recalibrated curve is found to be identical to the Hertz equation.

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Journal: TechConnect Briefs
Volume: 1, Nanotechnology 2012: Advanced Materials, CNTs, Particles, Films and Composites (Volume 1)
Published: June 18, 2012
Pages: 132 - 135
Industry sector: Advanced Materials & Manufacturing
Topic: Materials Characterization & Imaging
ISBN: 978-1-4665-6274-5