Extracting single-crystal elastic constants from polycrystalline samples using spherical nanoindentation and orientation measurements Dipen K. Patel a , Hamad F. Al-Harbi a,b , Surya R. Kalidindi a,⇑ a George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA b Mechanical Engineering Department, King Saud University, PO Box 800, Riyadh 11421, Saudi Arabia Received 12 March 2014; received in revised form 8 July 2014; accepted 8 July 2014 Abstract 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 con- structed 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 accu- racy and viability of the proposed approach are demonstrated for an as-cast cubic polycrystalline Fe–3% Si sample. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Spherical nanoindentation; Orientation imaging; Single-crystal elastic constants; Spectral representations; Finite-element models 1. Introduction Development of robust, physics-based, multiscale mate- rials models is significantly hampered by the lack of vali- dated tools and protocols for characterizing reliably the local (anisotropic) properties at length scales at or below the micron scale. Although numerical techniques such as the finite-element (FE) method have been shown to be suc- cessful in simulating complex interactions between micro- scale constituents of a composite material system [1–14], their predictive capabilities are strongly affected by assumptions made about the constitutive laws used to describe the local response of the microscale constituents present in these systems. It is often very expensive, and sometimes impossible, to produce sufficiently large volumes of the microscale con- stituents of interest in their pure form to allow the applica- tion of traditional mechanical testing methods (e.g. compression or tensile testing). One approach explored in the literature involves the fabrication of micropillars [15– 17] using a focused ion-beam and testing these pillars in a scanning electron microscope. However, this approach requires access to highly sophisticated equipment and is not particularly well suited for extracting the elastic prop- erties of the microscale constituents in composite material systems. In this paper, we present a new approach for estimating single-crystal elastic properties from polycrystalline http://dx.doi.org/10.1016/j.actamat.2014.07.021 1359-6454/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: surya.kalidindi@me.gatech.edu (S.R. Kalidindi). www.elsevier.com/locate/actamat Available online at www.sciencedirect.com ScienceDirect Acta Materialia 79 (2014) 108–116