## 3 Results and Discussion  
### Fatigue Crack Growth for Mode I Test  
At a minimum displacement of 1.8 mm, an increased load leads to rapid crack growth length in the initial cycles, indicating swift crack progression in the low cycle range (N \(<\) 10\({}^{4}\)) as testing commences at maximum displacement. The region of highest loading was also pinpointed. This rapid crack growth behavior, consistent across \(R\) values of 0.3 and 0.5, as depicted in Figure 8, shows that higher \(R\) values correspond to slower crack growth rates. This pattern differs from that observed in isotropic and notched specimens, where the crack growth rate typically increases with higher loads near \(R\) = 1 [29]. Such behavior in double cantilever beam (DCB) specimens is likely attributable to their low fatigue crack growth/delamination resistance and thin adhesive layers [30]. It is also observed that maximum displacement has a more pronounced effect on crack growth rate than high loading rate. At fatigue crack growth rates (\(da/dN\)) between 10\({}^{-4}\) mm/cycle and 10\({}^{-5}\) mm/cycle, the fatigue crack fracture energy rate, calculated using Equations (8) and (9), diminishes to the more cycles there are, as illustrated in Figure 9a-c. Consequently, crack growth decelerates in the high cycle range (\(N>\) 10\({}^{4}\)). However, the results of the three tests show that the crack growth rate increases overall as \(R\) = 1 approaches. The total crack growth length is larger as \(R\) = 0 approaches, but the ratio of crack length per cycle (\(da/dN\)) increases as \(R\) = 1 approaches. This is because the test was conducted based on the fracture toughness value at the critical point. If a more stable crack growth rate is to be obtained, it could be considered that a lower standard value rather than the critical fracture toughness standard should be used.  
\[G_{max}=\frac{3P^{2}C}{2b\Delta a}, \tag{8}\]  
\[\Delta C=\frac{\delta}{P}, \tag{9}\]  
Figure 8: Fatigue test crack length curve at different load ratios: (**a**) \(R\) = 0.1; (**b**) \(R\) = 0.3; (**c**) \(R\) = 0.5.  
Further analysis, in accordance with Paris's law across three regions, reveals varied fracture energy rates. At a critical fracture toughness \(G_{C}\) of 1.12 kJ/m\({}^{2}\), the fracture energy rate \(G_{pl}\) in the unstable state is 1.186 kJ/m\({}^{2}\), and \(G_{th}\) the almost crack-free state is at 0.12 kJ/m\({}^{2}\), as shown in Figure 10. For \(R=0.3\), the values of \(G_{C}\) is 1.12 kJ/m\({}^{2}\), \(G_{pl}\) is 1.13 kJ/m\({}^{2}\), and \(G_{th}\) is 0.134 kJ/m\({}^{2}\), as indicated in Figure 10. The slowest crack growth rate at \(R=0.5\) is illustrated in Figure 10.  
Across all \(R\) conditions, differences in crack growth characteristics are observed in Stable I, II, and III sections, as depicted in Figure 11. The fatigue crack growth test shape aims to emulate the defect morphology in wind blade adhesive joints under various conditions. This study's primary parameters are the material factors listed in Tables 4 and 5. These factors \(c1\) and \(c2\) are derived from the \(G_{max}\)-cycles curve relationship, while \(c3\) and \(c4\) are obtained from the \(-da/MN\)-\(G_{max}\) curve. Here, \(r1\) and \(r2\), representing the initial state crack characteristics and crack limit point characteristics, are calculated using the equations \(G_{th}/G_{c}=r1\) and \(G_{pl}/G_{c}=r2\), respectively.  
Figure 9: Cycles–fracture energy rate curve of fatigue test at different load ratios: (**a**) \(R=0.1\); (**b**) \(R=0.3\); (**c**) \(R=0.5\).  
Figure 11: \(\mathrm{da/dN}\)–fracture energy rate curve of fatigue test at total.  
Figure 10: \(\mathrm{da/dN}\)–fracture energy rate curve of fatigue test at different load ratios: (**a**) \(R\) = 0.1; (**b**) \(R\) = 0.3; (**c**) \(R\) = 0.5.