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Nanoindentation is an experimental technique widely used for the characterisation of the elastic modulus and hardness of materials. In particular, it is the technique of choice when the mechanical properties of heterogeneous materials are sought. This is especially relevant for polymer matrix composites or bulk polymers that exhibit surface gradients due to processing or oxidative aging. However, despite the advancements in the experimental equipment that allow for the efficient production of large maps of elastic or hardness properties on surfaces, analysing experimental data on polymers presents challenges. Indeed, the constitutive laws governing polymers are usually viscoelastic or viscoplastic, which means that the elastic modulus and hardness alone are insufficient to fully describe the behaviour of these materials.

While it is possible to do indentation creep, indentation relaxation, or even dynamic indentation tests, the behavioural laws used to analyse these force-displacement curves are usually phenomenological and mechanical properties obtained do not compare well with macroscopic properties measured in standard tests. To obtain the parameters of more realistic constitutive laws from nanoindentation data, it is necessary to use numerical identification processes that minimise the difference between the simulated and the experimental indentation curve by testing different sets of material parameters. The inverse analysis using finite element method to simulate the nanoindentation response and an optimisation algorithm is a method explored by some research teams for different material behaviours [1]. However, it was shown that the set of material parameters obtained through this analysis is often not unique, and different combinations of constitutive laws, indenter shapes and loading protocols are necessary to test in order to improve the solution [2].

In this context, cyclic indentation loading appears to be a promising way to improve the identifiability of viscoelastic behaviour. Previous experimental work on polymers has shown that this loading provides results qualitatively similar to macroscopic cyclic behaviour for different loading rates [3]. In this presentation, the identifiability of viscoelastic behaviour from cyclic nanoindentation loading will be addressed. A numerical optimisation procedure using a genetic algorithm and a finite element model of spherical indentation has been implemented. Before identifying the material parameters from the experiment, an extensive study of numerical re-identification was conducted to explore different optimisation strategies and the impact of mutation and crossover rates of genetic algorithm, the formulation of the objective function, and the number of parameters of the Generalised Maxwell law to identify. It was shown, for instance, that adding more loading cycles improves the quality of identification. The quality of identification from cyclic indentation tests was also compared to the identification from indentation creep tests. The results clearly show that the identification from cyclic loading provides material parameters closer to the given set. The best identification strategy was then used to identify the viscoelastic properties of polypropylene, a polymer known for its pronounced viscoelasticity. The first results are very encouraging, but they also indicate that a more complex viscoelastic constitutive law may be necessary to improve the superposition of experimental and numerical data. This path is currently under exploration.

1. V. Le Saux, Y. Marco, G. Bles, S. Calloch, S. Moyne, S. Plessis, P. Charrier, Identification of constitutive model for rubber elasticity from micro-indentation tests on natural rubber and validation by macroscopic tests, Mechanics of Materials, Volume 43, Issue 12, 2011, Pages 775-786, https://doi.org/10.1016/j.mechmat.2011.08.015.

2. M.C. Barick, Y. Gaillard, A. Lejeune, F. Amiot, F. Richard, On the uniqueness of intrinsic viscoelastic properties of materials extracted from nanoindentation using FEMU, International Journal of Solids and Structures, Volume 202, 2020, Pages 929-946, https://doi.org/10.1016/j.ijsolstr.2020.03.015 .

3. Smerdova, O., Pecora, M. & Gigliotti, M. Cyclic indentation of polymers: Instantaneous elastic modulus from reloading, energy analysis, and cyclic creep. Journal of Materials Research 34, 3688–3698 (2019). https://doi.org/10.1557/jmr.2019.289