Abstract
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 stress-strain 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.
Highlights
In situations of industrial accidents, military assaults and terrorist events, reinforced concrete components of building structures and elements of critical infrastructure can be exposed to a combined action of explosive loads and fire
The variability expressed by the coefficient of variation (COV) for yield stress y of general population of reinforcing bars is around 4–11% [20]
COV of the modulus of elasticity of reinforcement steels from the same population is equal to 3.3%
Summary
In situations of industrial accidents, military assaults and terrorist events, reinforced concrete components of building structures and elements of critical infrastructure can be exposed to a combined action of explosive loads and fire. A combined dynamic and thermal action on reinforced concrete structures is assessed by a coupled modelling of strain rate sensitive material properties and strength deterioration due to fire loading [1,2,3]. The practice of the coupled modelling of stress-strain relation of reinforcement bars is prevailed by the constitutive law known as the Johnson-Cook (JC) model [4, 5]. This model has been developed to consider the strain and strain rate hardening part of stress-strain relation and includes a component (singleparameter sub-model) accounting for thermal softening of steel. It is proposed how to fit components of the JC model by applying repetitive data that consists of a relatively small number of stress-strain records
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