# 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
#### 3.2.4 Comparison of Two Fatigue Life Prediction Methods  
Figure 13 presents a comparison of the predicted lives of CDM and CVGM with the test life. For the base metal specimen in Figure 13a, (1) the predicted crack initiation lives from the two methods are less than the test values, and the predicted accuracy is relatively near. The error between the predicted crack initiation life and the test value decreases with the increase in the strain range. (2) In the case of fracture life, the predicted value of CDM model is less than the test value, and the predicted result is safe; the predicted value of CVGM is larger than the test value, and the predicted result is unsafe. With the increase in the total strain range, the error between the predicted fracture life of CDM model and the test value decreases, whilst the error between the predicted fracture life of CVGM and the test value increases. (3) In the case of the predicted ratio of crack initiation life to fracture life, the ratio in the test exceeds 90%. The CDM model is more accurate in predicting the ratio than CVGM. For the weld specimen in Figure 13b, (1) the crack initiation life predicted by the CDM model is nearer the test value than that of CVGM, and the error between the crack initiation life predicted by the CDM and the test value decreases with the increase in the strain range. (2) In the case of predicting the fracture life of the weld specimen, the prediction results of the two methods are both less than the test values, and the error between the predicted fracture life by CDM and the test value is very small. (3) Similar to the base metal specimen, the ratio of crack initiation life to fracture life predicted by the CDM model is more accurate than that predicted by CVGM. The CDM model can predict the number of cycles to initial damage of the base metal and weld specimens, whilst CVGM cannot. The prediction results by the CDM model are shown in Figure 14. The number of cycles to initial damage of the cross-section centre of the base metal and weld specimens and the cross section edge of the base metal and weld specimens decrease with the increase in the strain range. The number of cycles to initial damage at the cross section centre of the base metal specimen is less than that at the cross section edge of the base metal specimen. Thus, the centre of the base metal specimen is the crack initiation point, and the edge of the base metal specimen is the crack fracture point. Similar to the base metal specimen, the number of cycles to initial damage at the centre of the weld specimen is less than that at the weld edge of the weld specimen. Figure 13: Comparison of predicted life of CDM and CVGM with test life. (**a**) Base metal specimen and (**b**) weld specimen. The prediction accuracy of fatigue life and the relationship between fatigue and fracture lives of the CDM model are better than those of CVGM. Given that the CDM must only perform the uniaxial monotonic tensile test of the notched round bar specimen and calibrate the plastic strain threshold under uniaxial stress \(\varepsilon_{th}\), the complexity of the parameter calibration process is simple. The finite element model is established, and the model can be used to predict the ULCF damage of the base metal and weld specimens. In addition, the CDM model can directly consider the influence of damage on the elastic modulus of materials and directly combine with the finite element software and is thus easy to apply in engineering. CVGM is a semi-empirical and -theoretical formula and requires many parameter calibration tests. Uniaxial monotonic tensile test and strain cyclic loading test must be performed to calibrate the damage degradation parameter and toughness parameter \(\eta\). Compared with the CDM model, more parameters are calibrated, which leads to greater error. When establishing the finite element model, the characteristic length should be determined by combining with the scanning results of the electron microscope scanner on the base metal specimen and the fracture of the weld specimen.