Simultaneous extraction of the elastic-plastic properties of a thin film and its substrate from an identifiability-based design of depth-sensing nanoindentation testing

Abstract

This work presents an approach to simultaneously identify reliable elasto-plastic properties of a 100 nm amorphous alumina film and plastic properties of its silicon substrate by the Finite Element Model Updating (FEMU) method, using exclusively nanoindentation P−h curves. A 2D axisymmetric finite element model simulates the nanoindentation tests, and the Young's modulus E, the initial yield stress σy and the hardening modulus Hp of the thin film, as well as the yield stress of silicon σys are the parameters to identify. This work relies on a numerical design of experiments carried prior to the identification process. It uses the sensitivity of the nanoindentation force to a variation of the parameters to define an identifiability indicator (I-index) based on the conditioning of the inverse problem. It reflects the stability of the potential solution of the inverse problem. I-index minimisation below a certain value allows to ensure a reliable identification by designing the best combination of experiments in terms of relevant information. I-index analyses values demonstrate that combining Berkovich and cube corner nanoindentation tests at two different indentation depths brings sufficient information to well-conditioned the inverse problem. Indeed, the increased penetration and the varied indenter tip shape induce differentiating factors which activates the substrate effect, or anvil effect, and allow the dissociation of the thin film plasticity from that of the substrate, and thus its identification. The identification procedure of the four parameters carried out with the designed dual nanoindentation test from several starting points reveals that the FEMU method converged to a unique solution. Lastly, the identified parameters are validated by confronting experimental and numerical (i) P−h curves of a Berkovich test on a bulk silicon sample and (ii) residual topographies using a 3D FEM of a Berkovich test on the composite system thin film – substrate.