Robust determination of cubic elastic constants via nanoindentation and Bayesian inference

Nanoindentation is a promising tool for advancing the estimation of single crystal elastic constants in multiphase materials. In this study, a novel protocol is presented that couples high-speed nanoindentation mapping with the Vlassak and Nix’s model and Bayesian inference simulations to statistically estimate the elastic constants of cubic materials. The originality lies in considering ratios of indentation modulus as input data. For cubic elasticity, these ratios depend solely on two dimensionless parameters, which can be chosen as the Zener ratio A and the directional Poisson’s ratio ν 〈 100 〉 . Using ratios mitigates the influence of experimental calibration parameters. Only two constants are varied in the Bayesian simulations, and the computation time is further reduced by employing an optimized Vlassak and Nix’s model. This approach has also the great advantage to bound the search domain of ν 〈 100 〉 and A directly from elastic stability conditions. Furthermore, the method efficiency allows for continuous variation of the uncertainty considered in the experimental moduli, leading to stabilized Bayesian inference results. The choice of the finally retained values is thus simplified, converging to the uniqueness of the single crystal elastic constants. This method is successfully applied to high-purity Ni and Inconel 718, with the predicted elastic constants aligning well with literature data.