Statistical Analysis of the Dynamic Performance of Reinforcement Steel at Elevated Temperatures: The Case of Johnson-Cook Model

Description of mechanical properties of reinforcement steel by means of mathematical models known as constitutive laws is considered. The attention is focussed on the Johnson-Cook (JC) model developed to express the stressstrain relation by considering the coupled effect of strain and strain rate hardening as well as thermal softening of steel. The JC model is analysed due to its prevailing role in the practice of constitutive relation of properties of reinforcement steels. The key element of this study is a new look at the JC model from the statistical viewpoint. The JC model is subjected to examination by confronting its deterministic nature with statistical variability of experimental data that can be acquired from stress-strain records. It is stated that to now this variability has been largely ignored. The current practice of fitting the JC model to individual and non-repetitive stress-strain records is analysed. It is suggested how to address the problem of the model fitting in the case where stress-strain data is obtained by repetitive measurements. A procedure for processing small-size statistical samples extracted from this data is proposed. The essential idea of this procedure is to fit components of the JC model to limits of one-sided confidence intervals calculated by means of the statistical technique known as bootstrap resampling.