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.