An improved methodology for extracting uniaxial stress–strain curves from spherical indentation data

Abstract

In the recent years, it has been shown that the Pathak–Kalidindi (P–K) spherical indentation protocol and its accompanying definition of the indentation strain has many advantages over the classical definition. In the present work, an improved methodology to obtain the uniaxial stress–strain curve from the spherical indentation stress–strain curve is proposed based on the P–K protocol. The classical definitions of the representative strain, ϵruni, which relates the indentation strain to an equivalent uniaxial strain, and the non-dimensional strain, ϵND, which relates the indentation strain to the uniaxial stress, are revised in this work. These revisions are made such that they are consistent with the P–K protocol, and are shown to have the similar relationships as the classical equations. Using non-dimensional analysis, a closed form expression is obtained for the uniaxial stress as a function of the elastic–plastic properties of the material and the indentation strain. Based on this expression, an inverse approach is then utilized using results of finite element simulations to develop a methodology to predict uniaxial stress–strain curves from spherical indentation data for a large range of elastic–plastic mechanical properties. This methodology is demonstrated on spherical indentation stress–strain curves obtained from a set of finite element simulations for materials with mechanical properties spanning those of widely used structural alloys. Finally, this method is shown to provide good estimates of the uniaxial stress–strain curves from experimental spherical microindentation tests.