Bayesian Sequential Design of Experiments for Extraction of Single-Crystal Material Properties from Spherical Indentation Measurements on Polycrystalline Samples

Abstract

This paper explores a formal strategy for the extraction of single-crystal elastic constants of cubic polycrystalline metals based on the optimal design of spherical indentation experiments. Recent work has formulated the extraction of elastic constants using a two-step protocol. The first step established a surrogate model to capture the dependence of the indentation elastic modulus on the grain (i.e., crystal lattice) orientation and values of single-crystal elastic constants. The second step involved the use of Markov chain Monte Carlo to establish distributions on the elastic constants consistent with experimentally measured indentation moduli in grains of different orientations. The present study refines the second step in order to sequentially identify specific grains that should be indented to provide the most utility in improving the estimated distributions on the elastic constants. The proposed workflow is demonstrated for the extraction of elastic constants for an as-cast cubic polycrystalline Fe-3%-Si sample.