Estimation of directional single crystal elastic properties from nano-indentation by correlation with EBSD and first-principle calculations

Abstract

In this study, a two-step optimisation process for the estimation of the single crystal stiffness tensor from the indentation modulus is presented. This was accomplished by using a 2-dimensional data correlation method for nano-indentation, EBSD and ab initio data, as well as EDS for phase separation in a multi-phase material. Here, a single-phase Fe-24Ni-0.4C austenitic steel and a two-phase Fe-9.5Ni-0.5Co Seymchan meteorite were used as example materials.In a first step, the combination of high-speed nano-indentation mapping data with elemental and orientation distribution maps allowed the estimation of indentation moduli along specific crystal surface planes normal directions, (001), (011) and (111) using a least squares optimisation based on starting values from DFT or experimentally determined stiffness tensors. A second global optimisation step to estimate the single crystal stiffness tensor using pre-solved solution parameters of the Vlassak-Nix equations yielded reasonable correspondence between the experimentally determined stiffness tensors from correlative nano-indentation data and other methods. The presented method demonstrates generally the possibility to derive directionally sensitive elastic properties from high-speed nano-indentation for cubic materials statistically.

Keywords

• Nano-indentation
• Stiffness tensor
• Least-squares optimisation
• Austenitic steel
• Meteorite
• DFT