In this study, spherical indentation tests were used to determine the uniaxial tensile properties of metals at elevated temperatures (200 °C, 400 °C, and 600 °C). Taking the difference between spherical indentation tests at room and elevated temperatures into consideration, the incremental and analytical models were used to determine material parameters ( σ0, Ep, and n) and thermal softening parameters ( Eeff and m) in the Johnson–Cook constitutive equation, respectively. A discussion on the stability of the analytical model proved that despite in relative complicated forms and with three intercoupling material parameters, the analytical model is still effective for tensile property calculation. From the investigation on the relationship between pm and pi, it was found that correlating coefficient ξ is actually a function of both indentation depth and material parameters, and thus, a regression function was proposed for a more accurate description of ξ. Effectiveness of the spherical indentation tests was verified through experiments on three steels, SA508, 15CrMoR, S30408, and one titanium alloy, TC21, which proved that the spherical indentation tests can provide both proof and tensile strength calculations with a maximum error around 15% at room temperature and within 20% at elevated temperatures, and thus satisfy the demands for engineering applications.
Method to determine the optimal constitutive model from spherical indentation tests
