A universal relationship between indentation hardness and flow stress

A new indentation hardness (H) approach to evaluating the true stress (σ)–true plastic strain (ε) constitutive behavior of materials is described. Extensive elastic–plastic finite element (FE) simulations were carried out to assess the relation between H and σ(ε). The analysis led to derivation of a universal relation between H and σ(ε) given by H ≈ 4.05(1–34.6 σflow/E)σflow, where σflow = σy + 〈σsh〉, 〈σsh〉 is the average strain hardening between ε = 0 and 0.1, and E is the elastic modulus. Experimental H–σflow data pairs for the large set of alloys are in reasonably good agreement with the model predictions, but the experimental σflow are slightly higher and more linearly related to H than predicted. The H–σflow relation provides insight into the large variation of the H/σy ratios that are observed for different materials, as well as the corresponding variation in the ΔH/Δσy ratios used to estimate Δσy due to changes in an alloy’s condition, such as that induced by irradiation, based on measurements of ΔH. Notably, combinations of tensile and hardness tests can be use to estimate the average strain hardening from ε = 0 to 0.1 in irradiated alloys that have very small uniform strains.