Fig 9 The experimental
lives17,45–53 versus the prediction results of the
proposed model for different life ratios
The residual life was predicted using the proposed and typical
cumulative damage models. The comparisons between the experimental
results and the predicted life are illustrated in Fig 10. Most
predictions of the proposed model fall into the error band of 1.5, and
all fall within the error band of 2(Fig 10(A)). The predicted lives of
the K-R model66, Miner’s rule, and Li
model44 tend to be lower than the experimental
results(Fig 10(B), (C), (D)), especially for DTD6836,
S45C29, and Maraging Steel49, the
strengthening effect of the above three materials is significant(Fig 2).
In addition, the proposed model was compared with the typical cumulative
damage models using the fatigue life prediction error
model68 that is expressed as:
where P error is the life prediction error in
logarithmic form, Nf t andNf p are the experimental and
predicted fatigue life. The mean and standard deviation of the
prediction errors were calculated to compare the predictive ability of
the models, and these values are listed in Table 4. The proposed model
provides better predictions compared to other models.
The accuracy of life prediction can be further improved by using
material-dependent parameters. However, the material-dependent
parameters A and m need to be obtained from experimental
data, which limits the application of the proposed model. Therefore it
is necessary to illustrate that universal parameters can provide
sufficient prediction accuracy for the collected data. Test results of
three materials were selected to compare prediction accuracy. Here tests
for each material contain more than three life ratios. The root mean
square(RMS ) of the prediction error was used to compare the
prediction accuracy of different parameters:
where n is the number of predictive lives. The RMS of the
prediction errors is listed in Table 5. It is evident that the
deviations between the predictions using different parameters are
limited, and the universal parameters can provide enough accurate
predictions.