A High Strain Rate Constitutive Model for High Strength Steels

Traditional constitutive models can only describe a parallel or divergent stress strain response at different strain rates. This paper presents a new constitutive model that can describe convergent, divergent or parallel stress strain patterns. The new model is a modification to the popular Johnson-Cook model. By comparison with the Johnson-Cook model using high strain rate data of seven high strength steels, the new model is evaluated. The results showed that the new model could adequately describe the stress strain relation at high strain rates for the seven steels. In addition, an empirical relationship between the parameters in the new constitutive model and quasi-static tensile data has been developed based on the analysis of several high strength steels. The equation requires only quasi-static data as the input and is capable of estimating flow stresses at high strain rates. The calculated stress-strain curves at high strain rates can be used as a first order approximation for design purposes when the experimental high strain rate data are not available. The empirical equation is also evaluated by comparing the errors with the Johnson-Cook model.