On the Relation between Indentation Hardness and the True Stress-strain

A new and powerful indentation hardness (H) approach to evaluating the true stress (σ)-true plastic strain (ε), σ(ε), constitutive behavior of materials is described. Since measurements of H intrinsically probe a wide-range of ε (up to ≈0.5) , accurate assessment of the corresponding yield (σy) stress and strain hardening [σsh(ε)] pose a significant challenge. Extensive elastic-plastic finite element (FE) simulations have been carried out to assess the relation between H and σ(ε). The simulations were based on both a wide variety of analytical σ(ε) relations, in the form of σ(ε) = σy + σsh(ε), as well as actual σ(ε) derived from data on a large number of alloys with a very wide range of constitutive behavior. The analysis led to derivation of a remarkable universal relation between H and σ(ε) given by H ≈4.05(1 + 34.6σflow/E)σflow, where σflow = σy + <σsh>, <σsh> is the average strain hardening between ε = 0 and 10%, and E is the elastic modulus. Note we use consistent MKS units of MPa for both H and σflow. The expression for H(σflow) also can be inverted to one describing σflow(H). Experimental σflowH data pairs based on this definition of σflow for the large set of alloys noted above with a very diverse range of σ(ε) are in excellent agreement with the model predictions. The σflowH 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 ∆H/∆σy ratios used to estimate ∆σy due to irradiation based on measurements of ∆H. Applications of the H/σflow relation, including both evaluating <σsh> in materials that have very low uniform strain capacity in standard tensile tests and measuring at σ(ε) high ε.