# Fatigue Crack Growth from Notches:
## 4 Results
### Comparison of Unnotched and Notched Specimens in Simulations with Contact  
Figure 11a-f plot \(\delta_{p}\) versus \(\Delta a\) for simulations with and without notch for the three material models studied here assuming both plane strain and plane stress states. Most of the trends observed without contact (Figure 7) also exist with contact. The notch reduces \(\delta_{p}\), i.e., has a protective effect on da/dN. Once again, the length of unnotched crack used for comparison included the size of the notch. The protective effect increases with notch radius but tends to disappear as the crack propagates from the notch. There is a convergence to the curve corresponding to the unnotched sample, which occurs when the notch effect disappears. However, with contact, there is a marked influence of stress state. For plane strain conditions, there is a sharp increase of \(\delta_{p}\) with \(\Delta a\). A relatively large propagation is required to converge the notched and unnotched curves, particularly for the larger values of notch radius (Figure 10a,c,e). Under plane stress conditions, the increase of notch radius reduces substantially \(\delta_{p}\), which means that it has a protective effect. The convergence of the curves is now much faster than for plane strain state, i.e., the notch affected zone seems to reduce substantially. The material does not seem to affect these trends. The V-shaped behavior, typically observed for short cracks growing from  
Figure 10: Influence of the presence of the notch and the contact at the crack flanks in the \(\delta_{p}\) versus \(\Delta a\) curves (notched cracked specimen): (**a**) AA6082-T6 under plane strain; (**b**) AA6082-T6 under plane stress; (**c**) AA7050-T6 with pure kinematic behavior under plane strain; (**d**) AA7050-T6 with pure kinematic behavior under plane stress; (**e**) AA7050-T6 with pure isotropic behavior under plane strain; and (**f**) AA7050-T6 with pure isotropic behavior under plane stress.  
notches, is not observed here, with the exception of AA7050-T6 with pure isotropic behavior and plane stress behavior with notch radius \(r=1\)mm. The increase of load level is likely to promote this behavior.  
Figure 11: Comparison of notched and unnotched geometries regarding the evolution of \(\delta_{p}\) versus \(\Delta a\) (notched cracked specimen): (**a**) AA6082-T6 under plane strain; (**b**) AA6082-T6 under plane stress; (**c**) AA7050-T6 with pure kinematic behavior under plane strain; (**d**) AA7050-T6 with pure kinematic behavior under plane strain; kinematic behavior under plane stress; (**e**) AA7050-T6 with pure isotropic behavior under plane strain; and (**f**) AA7050-T6 with pure isotropic behavior under plane stress.  
\(U^{*}\) was evaluated under plane stress conditions for the three tested material models and for the four notch radii. The development of \(U^{*}\) with \(\Delta a\), as exhibited in Figure 12a-c, is similar for all materials. \(U^{*}\) increases as the crack becomes longer, being the rate of increase higher for smaller values of \(\Delta a\). As the stress concentrations decrease, i.e., the notch radius increases, lower values of \(U^{*}\) are achieved. The highest values of \(U^{*}\) are observed in Figure 12c for AA7050-T6 with pure isotropic behavior while the lowest are found in Figure 12a for AA6082-T6. Higher values of \(U^{*}\) are reached in the unnotched specimen, except for AA6082-T6. However, the differences relative to the notched cracked specimens tend to be attenuated for higher \(\Delta a\). For plane strain state, \(U^{*}\) has a peak for lower values of \(\Delta a\) and quickly decreases after. Note that the percentage variation of \(\delta_{p}\) is significantly higher than the percentage variation of \(U^{*}\), because \(\delta_{p}\) increases nonlinearly with effective load range.