tensile stress from 439.5 MPa to 527.4 MPa, the cycles to failure
also decreases. Based on the data shown in Fig. 3a, a linear formula
for the life prediction of creep-fatigue is proposed as below.
Nf ¼ Nf0 kDt
tp
ð1Þ
where Nf0 is the fatigue life with no dwell time and k is a factor of
effective dwell time at a given maximum tensile stress. By fitting
the experimental data, factors of effective dwell time at different
maximum tensile stresses are obtained and presented in Fig. 3a.
The plot of predicted life vs. tested life is shown in Fig. 3b. Most
of the predicted results are extremely close to the test results, and
the correlation between predicted life and tested life is less than
1.36, i.e. all the data fall into a range within a scatter band of
±1.36, which indicates that the linear formula is valid and accurate
enough to predict the creep-fatigue life. It should be pointed out
that at the condition of Dt = 60 s and rmax = 527.4 MPa, the cycles
to failure is too small (Nf = 58 cycles) and its predicted life is beyond
the error range, thus this data is out of consideration in Fig. 3b.
The relationship between minimum creep rate and maximum
tensile stress with different dwell times is shown in Fig. 4a. The
minimum creep rates are obtained from the curves in Fig. 2, in
which the minimum slope of each curve represents the minimum
creep rate. It reveals that the minimum creep rate increases with
the increase of maximum tensile stress. Meanwhile, the minimum
creep rate also increases with the increase of dwell time. Fig. 4b
shows the plot of cycles to failure (Nf) vs. minimum creep rate
(_emin) at different dwell times and maximum tensile stresses. By fitting
these data, a power-law formula for the life prediction of
creep-fatigue is obtained, which is as follows.
Nf ¼ að _eminÞb ð2Þ
where a and b are material constants. Here a and b are determined
to be 6.8556 104 and 0.89443 in this test. From Fig. 4b, it is
found that all data are close to the fitting line of the power-law formula.
The plot of predicted life vs. tested life is shown in Fig. 4c. The
correlation between predicted life and tested life is less than 1.45,
i.e. all the data distribute within a range of ±1.45, which indicates
that the predicted data are in a good agreement with the test data.
Note that the life prediction of creep-fatigue (Eq. (2)) has a similar
expression to the Monkman–Grant relationship for creep life prediction
[21], i.e. both have a power-law relationship with the minimum
creep rate, implying that creep has a decisive contribution to
the creep-fatigue life in the tests. The loading time (tf = 20 s), positive
mean stress and dwell time at maximum tensile stress play
important roles on the creep behavior. Fan et al. [22] also had
derived a similar power-law formula for creep-fatigue life prediction,
in which the mean strain rate at half-life was the controlling
parameter. In this study, the minimum creep rate is introduced in
Eq. (2) for the creep-fatigue life prediction.