Extracting single-crystal elastic constants from polycrystalline samples using spherical nanoindentation and orientation measurements

This paper describes a new approach for the extraction of single-crystal elastic stiffness parameters from polycrystalline samples using spherical nanoindentation and orientation measurements combined with finite-element (FE) simulations. The first task of this new approach involves capturing efficiently the functional dependence of the indentation modulus on the lattice orientation at the indentation site and the unknown single-crystal elastic constants. This step is accomplished by probing the function of interest using a suitably constructed FE model of spherical indentation, and establishing a compact spectral representation of the desired function using the discrete values obtained from the simulations. Note that this function needs to be established only once for a selected crystal lattice symmetry. In the second step of the approach presented here, the unknown single-crystal elastic constants for a selected phase are estimated through a regression technique that provides the best match between spherical nanoindentation measurements obtained on differently oriented grains of that phase in a polycrystalline sample (measured by orientation imaging) and the function established in the first step. The accuracy and viability of the proposed approach are demonstrated for an as-cast cubic polycrystalline Fe–3% Si sample.