Method to determine the optimal constitutive model from spherical indentation tests

The limitation of current indentation theories was investigated and a method to determine the optimal constitutive model through spherical indentation tests was proposed. Two constitutive models, the Power-law and the Linear-law, were used in Finite Element (FE) calculations, and then a set of indentation governing equations was established for each model. The load-depth data from the normal indentation depth was used to fit the best parameters in each constitutive model while the data from the further loading part was compared with those from FE calculations, and the model that better predicted the further deformation was considered the optimal one. Moreover, a Yang’s modulus calculation model which took the previous plastic deformation and the phenomenon of pile-up (or sink-in) into consideration was also proposed to revise the original Sneddon-Pharr-Oliver model. The indentation results on six materials, 304, 321, SA508, SA533, 15CrMoR, and Fv520B, were compared with tensile ones, which validated the reliability of the revised E calculation model and the optimal constitutive model determination method in this study. Keywords: Optimal constitutive model, Spherical indentation test, Finite Element calculations, Yang’s modulus