# Study on the Prediction Method of the Ultra-Low-Cycle Fatigue Damage of Steel
## 3 ULCF Life Prediction for the Q345 qC Base Material and Weld Joints
### ULCF Predictions for Base Material and Weld Joints
#### 3.2.3 Fatigue Life Prediction Based on the CVGM  
The CVGM is used to predict the damage of ULCF for base metal and weld specimens under cyclic loads. On the basis of the calibrated parameters, such as toughness parameters \(\eta\) and damage degradation parameter \(\lambda_{CVGM}\), the finite element model is combined with CVGM. The finite element model is similar to CDM, as shown in Figures 3 and 6. The developments of the fracture index \(F_{CVGM}\) of CVGM for the base metal and weld specimens are shown in Figures 11 and 12. At the same strain level, the fracture index \(F_{ICVGM}\) at the centre of the section grows faster than that at the edge. Thus, the cracks predicted by CVGM are generated at the centre of the section. At the same strain level, the damage index \(F_{ICVGM}\) of the weld specimen increases the fastest in the weld metal zone, followed by that of HAZ and nearly no growth is observed in the base metal. Therefore, the predicted fatigue cracks start in the weld metal zone, whilst nearly all the fatigue cracks of the weld specimen start at the section edge of HAZ in the test. The above-mentioned analysis shows that the fatigue crack initiation point of the base metal and weld specimens predicted by CVGM is inconsistent with the test. The predicted life is compared with the test values, as shown in Tables 8 and 9, to further demonstrate the accuracy of CVGM in predicting the ULCF life. \(N_{f,C}^{P}\) and \(N_{f,E}^{P}\) are the prediction fatigue lives at the cross section centre and edge, respectively. \(N_{f}\) and \(N_{r}\) are the test fatigue and fracture lives, respectively. \(N^{p}_{f}\) and \(N^{p}_{r}\) are the predicted fatigue and fracture lives, respectively. The predicted fatigue lives of weld metal \(N_{f,\text{WM}}^{p}\) and HAZ \(N_{f,\text{HAZ}}^{p}\) can be considered the predicted fatigue  
Figure 11: Development of the fracture index \(F_{ICVGM}\) of base metal specimen. (**a**) 7% and (**b**) 10%. Figure 12: Development of the fracture index \(F_{ICVGM}\) of weld specimen. (**a**) 7% and (**b**) 10%. and fracture lives, respectively. For the base metal specimen in Table 8, the predicted value of \(N_{f,C}^{p}\) is less than the test fatigue life \(N_{f}\) in all strain ranges. Moreover, the error of the predicted fatigue life to the test fatigue life decreases with the increase in the strain level. However, the predicted fracture life of the base metal specimen is greater than the test fatigue life, and the predicted results are relatively dangerous. For the weld specimen in Table 9, the predicted fatigue life \(N_{f,\text{WM}}^{p}\) is less than the test fatigue life \(N_{f}\), and their relative error is greater than that of the base metal specimen. Predicted fracture life \(N_{f}\) is opposite that of the base metal specimen and less than the test value. Table 10 shows the comparison results between the value of \(N_{f}^{p}\)/\(N_{r}\) calculated by CVGM and the test value of \(N_{f}\)/\(N_{r}\). Table 10 indicates that the ratio of the predicted crack initiation life to the fracture life is 71.4%-78.6%, which is less than the ratio of 91.7%-94.6% in the test, with a large difference. For the weld specimen, Table 11 shows that the CVGM-predicted value of \(N_{f}^{p}\)/\(N_{r}\) is 63.0%-69.2%, which is less than the test ratio of 87.5%-96.3%, and the error of both is more than that of the base metal specimen. The above-mentioned analysis indicates CVGM can predict the fatigue life (with also the crack initiation life) and fracture life but cannot predict the relationship between fatigue and fracture lives,