# Creep-Fatigue Behavior and Life Prediction of Medium-Si-Mo Ductile Iron
## 3 Results and Analysis
### Creep-Fatigue Interaction Behavior  
#### 3.2.1 Stabilized Cyclic Response Characteristics Under Creep-Fatigue Interaction  
Figures 5-7 compare the nominal stabilized hysteresis loops under creep-fatigue interaction with the corresponding low-cycle fatigue hysteresis loops at various temperatures and strain amplitudes.  
According to Figures 5-7, the hysteresis loop yield radius and elastic modulus are essentially unchanged during the loading and unloading stages after applying a hold time. Additionally, the creep-fatigue hysteresis loops are slightly higher than the low-cycle fatigue hysteresis loops. This is because the presence of creep causes the stress-strain response to reach the yield faster during reverse loading compared to LCF. Under the same total strain during reverse loading, the creep-fatigue condition experiences more inelastic strain, resulting in higher peak stress. This phenomenon manifests as an upward shift in the yield center of the hysteresis loops [27].  
Figure 4: The strain–life relationships of the ductile iron material at various temperatures: (**a**) RT, (**b**) 400 \({}^{\circ}\)C, (**c**) 600 \({}^{\circ}\)C, and (**d**) 700 \({}^{\circ}\)C.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Temperature (\({}^{\circ}\)C)** & \(\sigma^{{}^{\prime}}_{f}\) **(MPa)** & \(b\) & \(\varepsilon^{{}^{\prime}}_{f}\) & \(c\) \\ \hline RT & 664.95 & \(-\)0.054 & 0.658 & \(-\)0.786 \\
400 & 540.36 & \(-\)0.049 & 0.095 & \(-\)0.528 \\
600 & 299.00 & \(-\)0.100 & 0.170 & \(-\)0.541 \\
700 & 99.45 & \(-\)0.037 & 0.805 & \(-\)0.726 \\ \hline \end{tabular}
\end{table}
Table 3: Model parameters of medium-silicon molybdenum ductile iron at different temperatures.  
Nominal stabilized hysteresis loops of the ductile iron under various creep-fatigue conditions are shown in Figure 8. To enhance clarity, different colors and line styles are used to distinguish between different conditions.  
In Figure 8, it can be observed that changes in the strain amplitude do not significantly alter the overall shape of the hysteresis loops. The peak and valley stress values at small strain amplitudes generally fall near the stress values corresponding to larger strain amplitudes, indicating that creep-fatigue interaction does not substantially affect this material's plastic constitutive relationship. Regarding the influence of the hold time, the duration has a minor effect on the shape of the hysteresis loops. The primary reason for this is that the stress relaxation during the initial stage of the hold period is greater than that during the other stage. Consequently, the additional stress relaxation from longer hold times is relatively small, resulting in a minimal impact on the loop shape. However, if the hold time were substantially increased beyond the current experimental conditions, the incremental stress relaxation would become more pronounced compared to the shorter hold times, leading to more noticeable changes in the hysteresis loop shape. Additionally, it is evident that the stress relaxation per unit time gradually decreases with a prolonged hold time, meaning that the influence of the hold time on the loop shape diminishes over time.  
Figure 5: Comparison of creep–fatigue and LCF hysteresis loops at 400 \({}^{\circ}\)C under different strain amplitudes. (**a**) Strain amplitude of 0.3% and (**b**) strain amplitude of 0.4%.  
Figure 6: Comparison of creep–fatigue and LCF hysteresis loops at 600 \({}^{\circ}\)C under different strain amplitudes. (**a**) Strain amplitude of 0.2% and (**b**) strain amplitude of 0.4%.  
Figure 7: Comparison of creep–fatigue and LCF hysteresis loops at 700 \({}^{\circ}\)C under different strain amplitudes. (**a**) Strain amplitude of 0.2% and (**b**) strain amplitude of 0.4%.