## 1 Introduction  
Super duplex stainless steel SAF2507 is widely used in the oil and gas industries, especially in onshore pipelines and oil and gas transmission systems due to its excellent strength and corrosion resistance. In practical engineering applications, when pipelines were exposed to external cyclic loads, such as during the startup and shutdown of thermomechanical cycles, or when there were complex cyclic road vibrations, axial compressive strains in the pipeline could occur, with a gradual accumulation of plastic strains, resulting in a ratcheting effect that could seriously affect the safety and reliability of the components [1]. The study of the ratcheting behavior of SAF2507 stainless steel could be carried out using experimental analysis and the establishment of numerical calculation constitutive models to ensure the stable operation of the pipeline. A large number of theoretical and experimental investigations into the ratcheting behavior of metals have been conducted. [PERSON] et al. [2] studied how stress cycles and internal pressure influence the ratcheting behavior as well as the fatigue life of 1 Cr18 Ni10 Ti tubing; [PERSON] and [PERSON] [3] studied the mechanical characteristics and ratcheting behavior of 316H steel; [PERSON] et al. (2016; 2017) carried out ratcheting experiments on S45C steel, 63 Sn, and 37 Pb solder, respectively, and paid special attention to the ratcheting behavior at various loading rates, analyzing the effects of cyclic load, cyclic stress rate, and loading sequence on the ratcheting effect of the materials, respectively; and [PERSON] et al. (2016, 2017) conducted uniaxial cyclic stress tests on heat-treated 42 CrMo steel to investigate ratcheting strain and fatigue failure and their interaction. The construction of equipment pipelines and pressure vessels took into consideration the generation of ratcheting behavior (2016; 2017; 2018; 2019). Therefore, due to the limitations of the experimental information, it is equally important to discuss ratcheting strain theoretically. Elastoplastic constitutive models could be divided into coupled (2017) and uncoupled models (2018; 2019). The coupled class of models outperformed the uncoupled models in predicting ratcheting effects through the use of strain reinforcement and dynamic recovery terms and was widely used. The ratcheting effect of structures under diverse conditions requires a robust constitutive model, which can precisely express the mechanical response of materials subjected to cyclic loads. So far, many scholars have carried out a great deal of research work on this subject. For example, [PERSON] (2018; 2019; 2020) determined some classical cyclic constitutive models. [PERSON] (2018, 2019) proposed the concept of the criticality of dynamic recovery, [PERSON] and [PERSON] (2019) proposed an improved Ohno-Wang model incorporating the tension-pressure asymmetry, and [PERSON] (2019) improved the kinematic hardening law, drawing inspiration from [PERSON]'s ideas (2019). [PERSON] and [PERSON] (2019, 2021) introduced the non-proportionality of the load into the normal vector of the yield surface. [PERSON] (2019) considered the Dirac delta function to model deviation effects, and [PERSON] and [PERSON] (2019) and [PERSON] et al. (2020) introduced viscoplastic flow rules into the kinematic hardening model. [PERSON] (2019) applied the OW-I rate-independent model to study the ratcheting behavior of S30408, [PERSON] (2019) adopted a double-surface nonlinear kinematic hardening rate-independent model to analyze the ratcheting behavior of SAF2507 pipelines, and [PERSON] (2019) utilized the A-V rate-independent model to simulate the ratcheting effect of the austenitic stainless steel Z2 CND18.12N pipelines. Numerous researchers (2019; 2020; 2021; 2022) also revised constitutive models by relating various parameters. The new constitutive model (2019; 2021) was embedded by the researchers into a simulation software to predict ratcheting deformation, which produced good simulation results.