# Creep-Fatigue Behavior and Life Prediction of Medium-Si-Mo Ductile Iron
## 3 Results and Analysis
### Creep-Fatigue Interaction Behavior
#### 3.2.2 Investigation of Creep-Fatigue Life Prediction Models
(a) The net tensile hysteresis energy in LCF processes, (b) the LCF net tensile hysteresis energy under creep–fatigue interaction, and (c) the inelastic strain energy during creep processes. Based on the creep test results, the relationship curves (\(\hat{w}_{in}-w_{f}\)) and corresponding parameter fitting results for medium-silicon molybdenum ductile iron at three different temperatures are presented in \[d_{c}=\int_{0}^{t_{c}}\frac{1}{t_{R}}\ \mathrm{d}t \tag{4}\]8  
As shown in Figure 11, for medium-silicon molybdenum ductile iron at 400 \({}^{\circ}\)C, 600 \({}^{\circ}\)C, and 700 \({}^{\circ}\)C, when \(\hat{w}_{in}\) is below 0.02 MJ/m\({}^{3}\)/s, 0.015 MJ/m\({}^{3}\)/s, and 0.01 MJ/m\({}^{3}\)/s, respectively, \(w_{f}\) increases with increasing \(\hat{w}_{in}\) values. However, as \(\hat{w}_{in}\) continues to rise, \(w_{f}\) begins to stabilize or slightly decrease due to the reduced creep ductility of the material under high stress, as indicated by the dashed lines in \[d_{c}=\int_{0}^{t_{c}}\frac{1}{t_{R}}\ \mathrm{d}t \tag{4}\]9 Consequently, the critical inelastic strain energy density (\(w_{f,crit}\)) values for medium-silicon molybdenum ductile iron were determined to be 79 MJ/m\({}^{3}\), 24 MJ/m\({}^{3}\), and 11.5 MJ/m\({}^{3}\) at 400 \({}^{\circ}\)C, 600 \({}^{\circ}\)C, and 700 \({}^{\circ}\)C, respectively. Since the Feltham empirical formula was employed to characterize the stress relaxation process in this study, it was necessary to determine the relevant parameters in this formula. The fitting results are shown in Figure 12, and the parameters obtained under various conditions are listed in \[t_{R}(\sigma,T)=k_{TF}\cdot\sigma^{-\alpha_{TF}} \tag{5}\]0  
Based on the aforementioned parameters, the life prediction results of creep-fatigue interaction tests using both the TF and T-SEDE models are presented in Figure 13a,b, respectively. The failure criterion was defined as the cumulative sum of fatigue damage and creep damage reaching one. \[t_{R}(\sigma,T)=k_{TF}\cdot\sigma^{-\alpha_{TF}} \tag{5}\]1 Relationship between instantaneous inelastic strain energy density dissipation rate and inelastic strain energy density for medium-silicon molybdenum ductile iron at various temperatures. \[t_{R}(\sigma,T)=k_{TF}\cdot\sigma^{-\alpha_{TF}} \tag{5}\]2 Experimental data and curve fitting of stress relaxation at different temperatures: (a) 400 \({}^{\circ}\)C, (b) 600 \({}^{\circ}\)C, and (c) 700 \({}^{\circ}\)C.  
Regarding the TF model shown in Figure 13a, the predictions yielded relatively satisfactory results at 600 \({}^{\circ}\)C, with all data points falling within the 2\(\times\) scatter band. However, the predictions were less accurate at other temperatures. Overall, the predictions across all temperatures tended to be conservative, with some data points at 700 \({}^{\circ}\)C approaching the 3\(\times\) scatter band. Notably, for one condition (400 \({}^{\circ}\)C, 0.4%, and 60 s), the prediction exceeded the 10\(\times\) scatter band. This discrepancy arose because the TF model considers creep to be solely dependent on stress and time, and according to Equation (5), life exhibits a power-law relationship with stress, meaning higher stress leads to a shorter life. In this study, this approach overestimated creep damage during the initial high-stress phase of the dwell period. Furthermore, even after stress relaxation stabilized during the prolonged dwell times, creep damage continued to accumulate. For stress relaxation that maintained relatively stable higher stress levels during the dwell period, the relatively high stable stress resulted in overestimated creep damage, leading to conservative predictions. In contrast, the T-SEDE model presented in Figure 13b employs a strain energy density dissipation approach based on the relationship between material failure and energy. This model incorporates [PERSON]'s concept of creep damage immunity at higher inelastic strain energy density dissipation rates, resulting in more accurate predictions compared to the TF model.