## 2 Determination of Chaboche Material Parameters
### Experiment Results and Discussion  
The result from the stabilized uniaxial strain control test is illustrated in Figure 6a,b. Figure 6a demonstrates the cyclic hardening in the strain-symmetric cyclic history. The hysteresis loop tends to limit itself to a closed stable loop after a number of cycles. The hysteresis loop is stabilized after eleven cycles in which the pipe exhibits significant hardening before stabilization. In the subsequent strain symmetric cycling, the specimens are unloaded to zero magnitude of axial stress and strain. Figure 6b shows the final stabilized hysteresis loop of the test. The results of the monotonic tensile test and post-stabilized monotonic test are shown in Figure 7. The test was conducted for a strain range of 0 to +1.8% where the stress-strain plot exhibits strain hardening after the elastic limit. The yield points at 0.2% strain offset are calculated to be 264 MPa and 305 MPa for monotonic and post-stabilized monotonic test, respectively. Most of the ratcheting parameters are obtained from the monotonic, post-stabilized monotonic, and stab  
Figure 6: (a) Cyclic hardening behaviour of 316L stainless steel (b) stabilized hysteresis curve. Figure 8 depicts the stress-strain responses from the monotonic and post-stabilized monotonic test superimposed on the upper hysteresis curve result from cyclic test with symmetric strain control in the plastic region. The figure shows the effect of material hardening on the stabilization of stress-strain behaviour after several loading cycles. It can be observed that strain hardening causes a significant increase of the linear section of the post-stabilized monotonic test and the hardening is caused by cyclically stabilized axial strain symmetric cycling, rather than first half tension of strain control monotonic test. In the figure, the transient Bauschinger effect can be observed, which gives rise to a smaller plastic modulus in the stabilized hysteresis loop compared to the post-stabilized monotonic loading. This happens if the applied peak strain is relatively small in prior strain control hardening [36; 37; 38; 39]. The \"shifted curve\" in Figure 8 refers to the stress and strain data obtained in the upper or lower stabilized hysteresis loading. The shifted curve (\(\sigma_{\text{shift}},\epsilon_{\text{shift}}\))) obtained from upper curve is regularized by the following equations:  
\[\sigma_{\text{shift}}=\frac{1}{2}(\sigma_{\text{Upper curve}}-\sigma_{\text{Max at maximum strain control}}), \tag{1}\]  
\[\text{and}\ \ \epsilon_{\text{shift}}=\frac{1}{2}(\epsilon_{\text{Upper curve}}-\epsilon_{\text{Max at maximum strain control}}). \tag{2}\]  
Figure 8: Monotonic, post-stabilized monotonic curves, upper hysteresis curve and shifted curve of AISI 316 LS. Figure 7: Monotonic and post-stabilized monotonic curves of AISI 316 LS. From Figure 8, the knee section of the calculated shifted curve is positioned below the knee sections of monotonic and post-stabilized monotonic curves because the quasi linear segment of shifted curve is shorter in comparison to the monotonic and post-stabilized monotonic curves. Hence, the shifted curve, obtained from hysteresis curve, does not present the true mode of monotonic behaviour of the material. Figure 9 illustrates the stress-strain response of the uniaxial tests in which the subsequent maximum load is incremented by 4 MPa after every complete unloading. The loading-unloading process is continued when a large permanent axial deformation occurs. From the figure, for the cycle with maximum stress \(\sigma_{Max}\) of 244 MPa, the strain starts from 0 \(\mu\epsilon\) at zero load and remains 0 \(\mu\epsilon\) upon unloading. For the cycle with maximum stress of 248 MPa, the strain starts from 0 \(\mu\epsilon\) at zero load and retains 7.5 \(\mu\epsilon\) upon unloading. For the cycle with maximum stress \(\sigma_{Max}\) of 252 MPa, the strain starts from7.5 \(\mu\epsilon\) at zero load and reads 20 \(\mu\epsilon\) upon unloading.