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:
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ d}_{c}=\int_{0}^{\text{th}}{\frac{\dot{\varepsilon_{\text{in}}}}{\varepsilon_{f}(\dot{\varepsilon_{\text{in}}},\ T)}\text{dt}}\)⑺
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
\(d_{f}=\frac{1}{N_{f}}\) ⑻
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:
\(N_{p}=\frac{1}{d_{c}+d_{f}}\) ⑼
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.