## 6 Conclusions  
In this paper, Chaboche ratcheting model parameters for 316L stainless steel pipes were determined from experimental uniaxial and hysteresis loading. The parameters were optimized using two different multi objective intelligent optimization technics, namely, Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) methods. Experiments were conducted in which all test specimens were cyclically stabilized in a symmetric \(\pm 0.75\%\) strain control loading prior to the following tests-monotonic uniaxial test, incremental uniaxial test, uniaxial and biaxial ratcheting tests.  
The elastic limit, obtained from incremental uniaxial test, plays an important role in the accuracy of prediction of ratcheting rate. Two methods were adopted from which the elastic limit was extracted; the first from experimental stress-plastic strain hysteresis curve and the second from post-stabilized monotonic curve. The stress-plastic strain curve is also employed to find ratcheting parameters. Parameter \(\gamma_{3}\) is obtained using PSO and GA methods. A uniaxial ratcheting test was conducted to calibrate \(\gamma_{3}\) with uniaxial ratcheting rate simulation. The uniaxial and biaxial ratcheting simulations were validated with experiments. Based on the analysed data, the main results can be summarized as follows:  
Figure 19: Chaboche model of ratcheting simulation results using ratcheting parameters presented in Table 4. (**a**) Uniaxial ratcheting rate, (**b**) biaxial ratcheting rate.  
1. Tests on 316L austenitic steels show the presence of transient Bauschinger effect in upper hysteresis curve with of \(\pm 0.75\%\) symmetric strain hardening range in comparison with post-stabilized monotonic curve.
2. The efficiency of generating ratcheting parameters, in terms of \(MSE\) and optimization time, is better in the PSO method compared to GA.
3. The elastic limit obtained from the incremental uniaxial test after pre-hardening offers an improved uniaxial ratcheting prediction.
4. Compared to the hysteresis curve, the ratcheting parameters obtained from post-stabilized monotonic curve present more accurate ratcheting prediction.  
Most of the material parameters for ratcheting prediction models implemented in FEM software such as ANSYS and ABAQUS, are determined from the uniaxial hysteresis test curve. The current study presents parameter determination and calibration for subsequent implementation of Chaboche ratcheting model in ABAQUS and ANSYS. The current material parameters can be adopted for other ratcheting models such as Modified Chaboche, Ohno-Wang, Armstrong-Frederick-Ohno-Wang and Chen-Jiao-Kim (CJK). Since most of these models parameters are supposed to be obtained from hysteresis test curves, the present results can be compared with other ratcheting models predictions.  
[PERSON] and [PERSON] devised the project, the main conceptual ideas and the proof outline. [PERSON] carried out the experiment, performed the analytic calculations and performed the numerical simulations. [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] developed the theoretical formalism and performed the optimization. [PERSON], [PERSON], and [PERSON] wrote the manuscript. All authors provided critical feedback and helped shape the research, analysis and manuscript and contributed to the interpretation of the results.  
This research was funded by the Ministry of Education, Malaysia, under Grant. Nos. GUP/PY/2012/01341, FRGS/PY/2015/05594, GUP/PY/2015/05594, and FRGS/PY/2014/03315. One of the authors, [PERSON], also received funding from UTM under Grant. No. eScience/PY2014/03221.  
The authors declare no conflict of interest.