## 6 Results and Discussions  
The main results of the thermal-mechanical analyses performed on the throat regions are described in this paragraph. Figure 12 shows the temperature and the von Mises stress contour plots for the CuCrZr liner at the end of the purging phase, 0.3 s after starting the ignition phase, and at the end of it. The maximum temperature value of 545 K was still too small for the creep failure occurrence. Indeed, as shown in Figure 12, the lowest temperature value considered in the creep tests is about 100 K greater than the maximum temperature value obtained in the thermal analysis. Furthermore, the ligament compressive stresses in the tangential direction detected in the hot phase remain compressive up to the end of the creep period. Therefore, no creep failure evaluations were needed for the life assessment. On the other hand, creep failure can become dominant when higher thrust levels are required; in fact, higher pressure values are expected in the thrust chamber in this case. However, it is clear that creep relaxation strongly influences the stress-strain response of the structure, leading to an asymmetrical hysteresis curve, which is the cause of an accumulation of tensile plastic strains in the ligament (see Figure 13). Creep effects produce an upward trend of the stress-strain curve, leading to yielding in tension during the following purging phase. On the other hand, when creep is not modeled, the ligament tensile yielding could not occur and, in turn, a stabilization of the stress-strain curve could be envisaged after a few cycles, leading to a non-conservative estimation of the thrust chamber service life. Therefore, the creep modeling is crucial when studying the ratcheting behavior of the cooling channel. Particularly, primary creep effects, i.e., when creep deformation rate is not constant, are dominant with respect to secondary creep ones, especially in the first ten loading cycles. With regard to purging and ignition phases, a significant number of time steps were considered (see Table 9). This was due to their very small duration and because very high thermal gradients stresses could be reached especially in initial time intervals. Consequently, a coarse time discretization of these phases could lead to inaccurate results in terms of accumulated plastic strains. Plastic strains at the end of the ignition phase were reported in Figure 14. It was clear that the tangential strains were dominant with respect to other directions. However, the axial strains were non-negligible, since their maximum value was about one third of the maximum plastic strain in the tangential direction. This demonstrated the need to adopt a multiaxial fatigue criteria. Figure 12: Temperature and von Mises stress contour plots: (**a**) end of purging phase, (**b**) 0.3 s from the start of the ignition phase, (**c**) end of the ignition phase. Figure 13: Circumferential stress vs. time. Figures 15 and 16 show that the equivalent plastic strain increased cycle after cycle as a consequence of thermal ratcheting occurring in the ligament. The chosen kinematic hardening model with the three back stresses was capable of simulating ratcheting phenomena even after ten thermal-mechanical cycles. This result is in accordance with the results obtained in [3], showing that at least three Frederick-Armstrong kinematic hardening models should be considered when employing the Chaboche model, in order to properly allow for ratcheting. In fact, if just two hardening models were considered, the shakedown effect would anyway occur after very few cycles. A trendline was extrapolated from the FEM results and a stabilization of the equivalent plastic strains is expected to happen within 30-35 cycles, see Figure 16. As illustrated in Figures 15-17, the increment of plastic strain decreased cycle after cycle. Therefore, it is very likely that a stabilization of the stress-strain curve could occur, even though there is no assurance that it will happen.