The SS304 material, which includes 18 percent chromium and eight percent nickel, is the most widely-used austenitic stainless steel. It has good drawability and welding properties together with strong corrosion resistance. Austenitic stainless steel 08Ch18N10T is a chrome-nickel steel that is stabilized by titanium. This steel is widely used in the nuclear industry for piping systems and reactor internals in the Russian-designed VVERwater-water power reactors for nuclear power plants (NPP). Reactor internals are the part of an NPP that provides support, guidance, and protection for the reactor core and for the control elements. The block of guided tubes, the core barrel, the core barrel bottom, and the core shroud are some of the internal components that are exposed to very harsh operating regimes. The operating regime, e.g., heating and shut-downs, has a significant influence on the service life of the components. The vibration and pressure pulsation of the water pumps also have to be taken into account. These regimes expose the reactor internals to cyclic loading.
In practice, cyclic loading of structural parts can lead to the formation and propagation of cracks through the process referred to as fatigue. In all areas of industry, the operational safety of machinery depends on an appropriate design process, which includes an analysis of all possible critical states. In the low-cycle fatigue domain, seismic analysis and the simulation of operational tests of the piping systems of NPPs may be used as an example. In these cases, it is crucial to have an accurate description of the stress–strain behavior of the material that is being considered.
Phenomenological models [1
] are the most widely-used models in practical applications. Their goal is to provide an as accurate as possible description of the stress–strain behavior of the material, which is found on the basis of experiments [2
]. The stress–strain behavior of structural materials under cyclic loading is very diverse, and a case-by-case approach is required [3
The most progressive group of cyclic plasticity models, which are commonly encountered in commercial finite element method programs, is the single yield surface models based on differential equations. Their development is closely linked to the creation of a nonlinear kinematic hardening rule with a memory term, introduced by Armstrong and Frederick in 1966 for the evolution of back-stress [4
] and the discovery by Chaboche [5
] of the vast possibilities offered by the superposition of several back-stress parts.
Developments in the field of non-linear kinematic hardening rules were mapped in detail in [1
]. In the current paper, we will mention only the most important theories. In 1993, Ohno and Wang [6
] proposed two nonlinear kinematic hardening rules. For both models, it was considered that each part of the back-stress had a certain critical state of dynamic recovery. Ohno–Wang Model I leads to plastic shakedown under uniaxial loading with a nonzero mean axial stress value (no ratcheting), and under multiaxial loading, it gives lower accumulated plastic deformation values than have been observed in experiments. The memory term of Ohno–Wang Model II [6
] is partially active before reaching the critical state of dynamic recovery, which allows a good prediction of ratcheting under uniaxial loading and also under multiaxial loading. The Abdel-Karim–Ohno nonlinear kinematic hardening rule [7
] was published in 2000. This rule is in fact a superposition of the Ohno–Wang I and Armstrong–Frederick rules. The proposed model was designed to predict the behavior of materials that exhibit a constant increment of plastic deformation during ratcheting. Other modifications to this kinematic hardening rule, leading to a better prediction of uniaxial ratcheting and also multiaxial ratcheting, were proposed by one of the authors of the paper [8
]. In order to capture the additional effects of cyclic plasticity, the concept of kinematic and isotropic hardening has been further modified. Basically, the available theories can be divided into two approaches. The first approach is related to the actual distortion of the yield surface [9
], while the second approach is related to the memory effect of the material [5
]. The effect of cyclic hardening as a function of the size of the strain amplitude is usually assumed in the second approach.
The first comprehensive model of cyclic plasticity with a memory surface was proposed by Chaboche and co-authors in [5
]. Chaboche’s memory surface was established in the principal plastic strain space and captures the influence of plastic strain amplitude and also the mean value of the plastic strain. The memory surface is associated with a non-hardening strain region in a material point, as was explained by Ohno [12
] for the general case of variable amplitude loading. Memory surfaces established in the stress space have also been developed. Their main advantage is that they enable more accurate ratcheting strain prediction to be achieved, as presented by Jiang and Sehitoglu in their robust cyclic plasticity model [13
It should be mentioned that both of these memory surface concepts lead to an increase in the number of material parameters and in the number of evolution equations, which complicates their use in engineering practice.
The original application of the memory surface, introduced by Jiang and Sehitoglu, was extended by some authors of the present paper to capture the memory effect of ST52 material, in [14
]. Uniaxial experiments indicated that, in the case of a cyclically-softening/hardening material, larger strain amplitudes cause a significant change in the shape of the hysteresis loops. Only a very small number of researchers in the field of cyclic plasticity have investigated the influence of strain amplitude on the cyclic hardening effect. Good agreement with experiments has been achieved in the case of steel SS304 [15
], but at the cost of defining more than 70 material parameters.
Some of the material models have been used to capture cyclic material behavior. To describe the cyclic behavior of SAE4150 martensitic steel [16
], Schäfer et al. considered three kinematic hardening models, i.e., the Chaboche [5
], Armstrong-Frederick [4
] and Ohno–Wang [6
] models. They used these kinematic approaches to simulate the micromechanical behavior of the selected material. Moeini et al. [17
] used the Chaboche model [5
] to predict the low cyclic behavior of dual-phase steel. The selected kinematic hardening model provided good agreement with experimental results. Msolli used the unified viscoplastic model [18
] developed by Chaboche when modeling the elastoviscoplastic behavior of JLF-1 steel at higher temperatures (400
). In this study, the Chaboche model was slightly modified to capture cyclic hardening followed by cyclic softening. The material model also falls into the category of coupled damage models. The material model showed good agreement with the experimental results. The effect of torsional pre-strain on low cycle fatigue performance of SS304 was studied in [19
]. Kang et al. [20
] used the viscoplastic constitutive model with the extended Abdel-Karim–Ohno nonlinear kinematic hardening rule with some temperature-dependent terms. This constitutive model was verified on uniaxial and non-proportional multiaxial ratcheting experimental results at room temperature and at elevated temperatures. Another viscoplastic constitutive model was used by Kang, Gao, and Yang [21
] in their study to simulate uniaxial and multiaxial ratcheting of cyclically-hardening materials. They used the Ohno–Wang kinematic hardening rule with the critical state of dynamic recovery. The effect of loading history was also considered by introducing a fading memorization function for the maximum plastic strain amplitude.
This paper shows the advantages of using the memory surface established by Jiang and Sehitoglu in 1996 [13
] to treat the impact of the strain amplitude on the material stress response. The new theory is shown on the kinematic hardening rule based on Chaboche’s model with three back-stress parts, but it can also easily be applied to the Abdel-Karim–Ohno model or its modified version with promised ratcheting prediction [8
]. Recently, an approach was introduced that takes into account a new internal variable referred to as virtual back-stress, corresponding to a cyclically-stable material. This provides an easy way to identify the parameters and to use fewer material parameters than in earlier models, for example [21
]. New experimental results from uniaxial fatigue tests realized on 08Ch18N10T at room temperature are presented and subsequently used for the validation of the new cyclic plasticity model.