5. Life prediction
In terms of the life prediction of creep-fatigue tests, the methods based on stress control are obviously fewer than strain control due to the unclosed hysteresis loops.51,52 The ductility exhaustion approach in R553 is one of the wide-used life prediction methods of creep-fatigue tests under stress control, which describes the creep damage per cycle as:
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ d}_{c}=\int_{0}^{\text{th}}{\frac{\dot{\varepsilon_{\text{in}}}}{\varepsilon_{f}(\dot{\varepsilon_{\text{in}}},\ T)}\text{dt}}\)
where \(\dot{\varepsilon_{\text{in}}}\) is the inelastic strain rate of the material during the holding time per cycle, \(\varepsilon_{f}\) is the creep ductility of the material, which is usually related to the creep strain rate and temperature. Correspondingly, the fatigue damage per cycle is calculated by
\(d_{f}=\frac{1}{N_{f}}\)
where \(N_{f}\) is the fatigue life. When the sum of cumulative creep damage and fatigue damage is equal to 1, the failure is acknowledged and the predicted life of the creep-fatigue test is calculated as:
\(N_{p}=\frac{1}{d_{c}+d_{f}}\)
It should be noted that fatigue damage was confirmed to have little effect compared with creep damage under cyclic creep in present work. Hence, the term can be neglected, and the predicted result by the ductility exhaustion method of R5 is shown in Fig. 12. It can be found that the predictions are much lower than experimental results, and the error enlarges with the increasing observed cycles to failure. The predicted cycles to failure in the cases of long duration under valley stress are more outrageous, which are circled in red. The over-conservative prediction is generally due to the neglect of the anelastic recovery effect in cyclic creep.