A universal constitutive model considering strain range dependence effect and transient behaviour for both cyclic softening and hardening steels

High-temperature low-cycle fatigue (HTLCF) behaviour of 2.25CrMoV and 316L were investigated by employing internal stress. Results reveal that 2.25CrMoV and 316L show cyclic softening and hardening–softening behaviour, respectively. Moreover, they exhibit strain range dependence effect (SRDE) and transient Bauschinger effect (TBE). The SRDE of 316L was observed throughout the entire fatigue procedure, whereas that of 2.25CrMoV was only observed in the initial softening stage. It is noteworthy that the SRDE is controlled by both back and effective stresses in the case of 316L, and it is primarily dominated by the back stress for 2.25CrMoV. Based on the internal stress analysis, a universal constitutive model was developed. Compared with existing models, a cycle-dependent kinematic hardening factor φ was coupled into kinematic hardening variables to improve the description of the hysteresis loops. Besides, a unified modelling method for SRDE was developed based on a kinematic-isotropic combined hardening rule extended with a strain memory surface. Furthermore, a novel two-dimensional proportionality factor δ related to the plastic modulus of cyclic and monotonic responses was incorporated into the short- and medium-range kinematic hardening variables to account for TBE. Finally, the validity of the proposed model was discussed from the hysteresis loop, peak stress evolution, and peak internal stress evolution. The good agreement between experimental data and simulated results suggests that the proposed model is robust in predicting cyclic softening and hardening–softening behaviours.