Constitutive model for cyclic behavior of mild steel under various strain amplitudes

To enable accurate simulation of steel material under various loadings, cyclic behaviors of mild steel Q235 were extensively investigated through experimental analysis and constitutive modeling in this work. The studied steel was tested under cyclic loading protocols with constant strain amplitudes and variable strain amplitudes. The evolutions of stress amplitude, effective stress and back stress components, and elastic stiffness during the whole cyclic loading history are quantitatively scrutinized. The results demonstrate that mild steel exhibits cyclic capacity depended strongly on strain amplitude. Besides, the strain history effect depends on both the historical maximum strain amplitude and the target unloading strain amplitude, indicating the existence of a critical state for the incomplete evanescence of strain memory surface to be activated. An abrupt drop of effective stress at onset of plastic straining is observed in experimental tests and contributes to the early re-yielding of the reversed curve. Furthermore, elastic stiffness in the cyclic loading phase differs much from that in initial tension. Based on those observations, a new constitutive model with robust ability to predict hysteretic behavior of structural steel under complex loading paths is proposed. This model considers the strain range dependence and the strain history dependence effects. In addition, a new method to identify the yield points of hysteretic loops is proposed in this paper to enable simulations of back stress with the Armstrong-Frederick hardening model without considering the strain range dependence effect. The validity of this model is demonstrated through comprehensive comparison between simulated results and experimental data.