On the uniqueness of intrinsic viscoelastic properties of materials extracted from nanoindentation using FEMU

Instrumented nanoindentation is widely used to extract the material properties from the measured force-displacement curves. In this work, the uniqueness/non-uniqueness of the intrinsic viscoelastic properties of materials determined by nanoindentation during load-unload tests is investigated. A four-parameter viscoelastic law with constant Poisson's ratio is used to model the mechanical behavior of a polymer material and a 2D-axisymmetric Finite Element Model (FEM) is used to simulate the nanoindentation test. Firstly, a nanoindentation experimental triangular load-unload test is performed on a bulk sample of polypropylene (PP) with a Berkovich indenter tip at a depth rate of 1000 nm/min. The values of the four material parameters are estimated by the Finite Element Model Updating (FEMU). The numerical results can accurately fit the experimental data. However, several quasi-solutions are shown to exist. These load-unload data allow to identify only three viscoelastic parameters if the Poisson's ratio is known. Secondly, the effect of nanoindentation depth rate, loading type (triangular, trapezoidal, exponential, sinusoidal) and apex angle is numerically investigated using an identifiability index based on the conditioning of the inverse problem. We show a correlation between the identifiability index and the energy dissipated by the material during the tests. The extraction of all material parameters remains impossible using a single test. Finally, some combinations of several nanoindentation triangular tests and indenter tip angles are also investigated. We show that a dual nanoindentation technique (cube corner and Berkovich tips) with triangular load-unload tests is an interesting combination to reliably extract all the viscoelastic parameters, provided that plasticity is taken into account. This result illustrates the interest of using this numerical identifiability index to design nanoindentation experiments to ensure the robustness of the intrinsic viscoelastic properties extraction.