## 4 Calculation Results and Discussion
Among these, segments 0-0.349 and 0.651-1 are determined by the effective SIFs of the load contact position (3), while segments 0.349-0.651 are determined by the effective SIFs of the load contact position (4). In Figure 11b, after the initial depth of the 0.1 mm crack has propagated once, the maximum effective SIFs of the crack front are determined by the effective SIFs of the load contact position (3). In Figure 11c, after the initial depth of the 0.1 mm crack has propagated twice, the maximum effective SIFs of the crack front are determined by the effective SIFs of the load contact positions (3) and (5). In  
Figure 8: The SIFs of initial depth 0.1 mm crack front without propagation. (**a**) Position one; (**b**) position two; (**c**) position three; (**d**) position four; (**e**) position five. this case, segments 0-0.211 and 0.789-1 are determined by the effective SIFs of the load contact position (3), while segment 0.211-0.789 is determined by the effective SIFs of the load contact position (5). Figure 9: The SIFs of initial depth 0.1 mm crack front after the first propagation. (**a**) Position one; (**b**) position two; (**c**) position three; (**d**) position four; (**e**) position five. In Figure 12a, when the crack at the initial depth of 0.15 mm does not propagate, the maximum effective SIFs of the crack front are determined by the effective SIFs of the load contact positions (3) and (4). Among these, segments 0-0.211 and 0.789-1 are determined by the effective SIFs of the load contact position (3), while segment 0.211-0.789 is determined by the effective SIFs of the load contact position (5). In Figure 12b, after the initial depth of the 0.15 mm crack has propagated once, the maximum effective SIFs of the crack front are determined by the effective SIFs of the load contact position (3). In Figure 12c, after the initial depth of the 0.15 mm crack has propagated twice, the maximum effective SIFs of the crack front are determined by the effective SIFs of the load contact position (3). Figure 10: The SIFs of initial depth 0.1 mm crack front after the second propagation. (**a**) Position one; (**b**) position two; (**c**) position three; (**d**) position four; (**e**) position five. In Figure 13a, when the crack at the initial depth of 0.20 mm does not propagate, the maximum effective SIFs of the crack front are determined by the effective SIFs of the load contact position (3). In Figure 13b, after the initial depth of 0.20 mm, the crack propagated once, and the maximum effective SIFs of the crack front are determined by the effective SIFs of the load contact position (5). In Figure 13c, after the initial depth of 0.20 mm, the crack propagated twice, and the maximum effective SIFs of the crack front are determined by the effective SIFs of the load contact position (5). Figure 14 depicts the cycle life of crack propagation with varying initial depths. The joint simulation establishes the single propagation as the maximum crack front size at 0.02 mm. It is evident that the cycle life of the second propagation for each initial depth of the crack surpasses that of the first. Specifically, the second propagation cycle life of a crack with an initial depth of 0.1 mm is 7.52% longer than the first, the second propagation cycle life of a crack with an initial depth of 0.15 mm is 6.57% longer than the first, and the second propagation cycle life of a crack with an initial depth of 0.2 mm is 29.5% longer than the first. Additionally, it is observable that with the increase in the initial depth of the crack, the total life of the two extended cycles also experiences a significant increase. Notably, the cycle life of a crack with an initial depth of 0.15 mm increases by 20.4% compared to the 0.1 mm crack cycle life, and the cycle life of a crack with an initial depth of 0.2 mm increases by 25.2% compared to the 0.15 mm crack cycle life.