As mentioned above of various constitutive models
As mentioned above, of various constitutive models, the Chaboche kinematic model was widely used [3,7,, , , , ]. There exist many significant literature around the Chaboche/Chaboche type plasticity model calibration and its parameter determination methods. Aguis et al.  employed a multi-objective genetic algorithm to optimize the Chaboche model parameters to improve the accuracy of the fatigue life prediction for P3C aircraft components. Moreover, authors also conducted a sensitivity analysis for different workflows to assess what obviously influence the optimized parameter set, which acts as a guide on how to carry out a life prediction from kinds of test data. In Ref. , using a super-ellipse to combine two proposed objective functions, a multi-objective optimization method was developed based on the pareto front theory. Through optimization, the Chaboche type model captures the stress variation at different load histories. Based on genetic algorithm, Badnava et al.  developed an optimization method to identify the parameters of Chaboche combined hardening model for 304SS. With different loading conditions concerned, two dihydrochloride functions, from the relaxation and multi-step strain-controlled test, were naturally obtained. The optimized parameters are in good agreement with the experimental tests. Different from Ref. , in Ref.  a two-step optimization method was used to settle the parameters of the Chaboche kinematic hardening model according to the stress- and strain-based fitness functions. In summary, combining different fitness functions and multi-objective optimization methods can be used to purposefully obtain suitable Chaboche hardening model parameters for various loading conditions. Indeed, Chaboche et al. [14,32] recommended that, at least three A-F components should be incorporated in the model because this can improve the accuracy at different strain ranges, the goal cannot be achieved by using only one A-F component. Based on the aforementioned methodology, an optimization method was developed with the Levenberg-Marquardt algorithm in the current research. Different from the previous literature, just one fixed fitness function was applied to fit the stress- and strain-controlled experimental data. With a few trial calculations, a set of CHK-3-ISO-1 model parameters were obtained. Different from preceding literature [17,32,33], besides the third A-F hardening rule the second one has also influence the ratcheting, which is a fairly interesting conclusion for ratcheting simulation. Through this investigation, the strain-controlled cyclic mechanical behavior and ratcheting for 304SS are both properly described.
Research methodology The aim of this paper is investigating a set of Chaboche combined hardening parameters, which can be applied to simultaneously simulate the cyclic stress-strain response and ratcheting. For this purpose, the strain- and stress-controlled fatigue tests, as well as relevant numerical algorithms are all investigated herein. The main study procedures are schematically illustrated in Fig. 1.
Strain- and stress-controlled algorithm
CHK-3-ISO-1 model parameters identification and simulation
Conclusions The work is devoted to exploring the metallic ratcheting behavior based on Chaboche combined hardening model. One strain-controlled fatigue test was conducted by a step-by-step strain amplitude incremental method. In the test 304SS presents Masing-like behavior at strain range lower than 0.9%. To identify the CHK-3-ISO-1 model parameters, a strain-controlled test at strain range ±0.8% was carried out. Additionally, a ratcheting test with stress variation from −361.6Mpa to 441.6 MPa was performed. To reduce the stress overestimation at the ends of tensile/compressive curves, a pseudo-percent allocation method was proposed. Besides, two computational programs on the basis of strain- and the stress-controlled algorithm are developed to simulate respectively the cyclic mechanical behavior and the ratcheting strains. The detailed conclusions are listed in the following: