## 1 Introduction  
With excellent plasticity and toughness, S30408 austenitic stainless steel (type 304 stainless steel in American Iron and Steel Institute (AISI) materials designation) is often employed in the inner containers of LNG semi-trailer tanks [1]. In practical engineering applications, due to the complex road spectrum load and inertial forces, such as braking and steering, alternating stress is generated in the supporting regions of the inner container. The alternating stress together with the mean stress due to internal pressure becomes sufficiently high to make the material in this area encounter cyclic plasticity and produce gradual plastic strain accumulation, i.e., ratcheting. In the design of practical engineering structures, the cumulative damage caused by the ratcheting strain is an important issue to consider for the structural integrity [2]. Many scholars have produced extensive research on the ratcheting behavior of various materials and established a series of constitutive models. The classic Armstrong and Frederick (A-F) [3] model employed nonlinear characteristics due to the introduction of dynamic recovery of backstress and overpredicted ratcheting. [PERSON] [4; 5] described ratcheting with several A-F models. [PERSON] and [PERSON] [6; 7] introduced a critical state of dynamic recovery; however, multiaxial ratcheting prediction is yet be successfully demonstrated. Many scholars have modified and developed the constitutive model by associating different parameters [8; 9; 10; 11; 12; 13]. Cyclic softening and hardening can have a great influence on ratcheting in unsymmetrical stress cycles [14; 15]. The cyclic softening and hardening behaviors of materials are typically reflected in the isotropic hardening law of the model [16; 17; 18]. In order to improve the prediction of ratcheting strain of materials in the constitutive model, [PERSON] [19] modified the model proposed by [PERSON] and [PERSON], and embedded the cyclic hardening/softening characteristics of materials and additional hardening caused by non-proportional load into the Abdel-Karim model. [PERSON] et al. [20] introduced the evolution rule of function \(\phi(p)\) and the parameter \(\mu_{i}\) of material cyclic hardening or softening characteristics into the superposition model of the Ohno-Wang II model and A-F model, and improved the prediction effect of strain cyclic and uniaxial ratcheting strain. [PERSON] et al. [21] found that both isotropic hardening and kinematic hardening contributed to the cyclic softening of materials, and modified the Abdel-Karim and Ohno (AKO) model by quantifying the effects of isotropic hardening and kinematic hardening on the cyclic softening of materials. These studies demonstrated that different materials are of different ratcheting behaviors. S30408 is a metastable austenitic stainless steel. Under the influence of mechanical stress, plastic deformation and a cryogenic temperature service environment, martensitic transformation will be induced [22; 23; 24], resulting in significant changes in the mechanical behavior, thus, affecting the fatigue life of the materials. The high strength and toughness of S30408 stainless steel results from the transformation strengthening and plastic growth mechanism. Therefore, the influence of martensitic transformation should be considered in the establishment of a constitutive model. [PERSON] et al. [25] studied the plastic behavior of stainless steel at cryogenic temperatures, and put forward a constitutive equation including martensite volume fraction. [PERSON] et al. [26] found that cryogenic temperatures can improve the martensitic transformation rate of austenitic stainless steel AISI 316 LN. [PERSON] et al. [27] modified the expression of the martensite content by discussing different kinetic models of martensite transformation. Cryogenic temperature experiments of metastable austenitic stainless steel found that the martensite content in S30408 showed the rule of rapid growth first and then stability [28].