Determining effective radius and frame compliance in spherical nanoindentation

We estimate effective radii of a spherical nanoindenter at various indentation depths using Hertz elastic contact theory for the fully elastic contact region and AFM profiling residual indentation marks for the elastoplastic contact region. Using frame compliance measured as a function of indentation depth and the concept of infinitesimal deformation of a spherical nanoindenter, we introduce a profile of indentation–depth-dependent frame compliance that successfully explains the variation in frame compliance over the entire contact region. After using this indentation–depth-dependent frame compliance, we evaluated more consistent indenter radii from Hertz elastic contact theory at shallow indentation depths (<90 nm).

► We estimate radii of a spherical nanoindenter at various indentation depths.
► We introduce a profile of indentation–depth-dependent frame compliance.
► We successfully explained the effective radius of the spherical nanoindenter and frame compliance.