Indentation Analysis of Elastic-Plastic Homogeneous and Layered Media: Criteria for Determining the Real Material Hardness

A hardness analysis based on finite element simulation results and contact constitutive models is presented for both homogeneous and layered elastic-plastic media. The analysis provides criteria for obtaining the real material hardness from indentation experiments performed with spherical indenters. Emphasis is given on the estimation of the hardness of thin surface layers. The critical (maximum) interference distance that yields an insignificant effect of the substrate deformation on the estimation of the layer hardness is determined from the variation of the equivalent hardness of the layered medium with the interference distance (indentation depth). A relation between hardness, yield strength, and elastic modulus, derived from finite element simulations of a homogeneous half-space indented by a rigid sphere, is used in conjunction with a previously developed contact constitutive model for layered media to determine the minimum interference distance needed to produce sufficient plasticity in order to ensure accurate measurement of the material hardness. An analytical approach for estimating the layer hardness from indentations performed on layered media is presented and its applicability is demonstrated in light of finite element indentation results for an elastic-perfectly plastic layered medium with a hard surface layer.