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An experimental evaluation of the constant β relating the contact stiffness to the contact area in nanoindentation

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, Er . This relationship is often written in the form S=2βEr (A/π)1/2, where β is a constant that depends on the geometry of the indenter. Although the most common values for β 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 β 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° (cube corner) to 85.0°. The results are important in the accurate measurement of mechanical properties by nanoindentation