Measuring the elastic properties of anisotropic materials by means of indentation experiments

Abstract

The unloading process in an indentation experiment is usually modeled by considering the contact of a rigid punch with an elastically isotropic half space. Here we extend the analysis to elastically anisotropic solids. We review some of the basic formulae for describing the indentation of elastically anisotropic solids with axisymmetric indenters. We show how the indentation modulus can be calculated for arbitrary anisotropic solids and give results for solids with cubic crystal symmetry. We have calculated the contact stiffness for a flat triangular punch on a half space for various anisotropic materials. The indentation modulus for a triangular indenter is typically 5–6% higher than that for an axisymmetric indenter and varies only slightly with the orientation of the indenter in the plane of the indentation. We have conducted microindentation experiments to measure the indentation moduli of differently oriented surfaces of both cubic and hexagonal single crystals. For copper and β-brass, the (111) indentation moduli are approximately 10 and 25% larger than the {100} modulus. The (110) moduli are typically slightly smaller than the (111) moduli. The indentation modulus of zinc varies by as much as a factor of two, depending on the sample orientation. The hardnesses of the single crystals do not vary much with the orientation of the plane of indentation. For /gb-brass, the hardness of a {110} surface is only about 13% lower than the hardness of a {100} or {111} surface; for copper, the {110} hardness is 6% higher than for the other orientations. For zinc the maximum change in hardness with orientation is 20%.