Simple estimation method for strain rate sensitivity based on the difference between the indentation sizes formed by spherical-shaped impactors

Abstract

Abstract The Johnson-Cook (JC) flow stress model is widely used in finite element analysis (FEA) in various fields to express the deformation behavior of metallic materials under high strain rate conditions. There is a need to facilitate an easier estimate of the JC parameter C, which is a material constant in the JC model associated with strain rate sensitivity. In this study, a simple estimation method for the JC parameter C, based on the difference between the indentation sizes formed by two spherical-shaped impactors, was proposed. The proposed method allows us to estimate the JC parameter C only by measurement of the indentation sizes formed via a high-velocity impact test, a drop impact test, or an indentation test. The fundamental equation was theoretically derived based on the energy conservation during the impact process of the impactor and the expanding cavity model, combined with the JC model and the equation of thermal conduction. To validate the proposed method, FEA was conducted using ten types of target materials under five impact velocity conditions, from 6\xa0×\xa010−6 to 180 m/s. Based on the indentation depths obtained from FEA, the JC parameter C was estimated and compared with that input into FEA. As a result, it was confirmed that the estimated C is in agreement with that input into FEA within the relative errors of 10% under all impact velocity and target material conditions, except the target material of Ti6Al4V. From the results, it was demonstrated that the proposed method can easily estimate the JC parameter C, that is, the strain rate sensitivity, in the wide range of strain rate from 102 to 105 s−1.