# Fatigue Crack Growth from Notches:
## 4 Results
### Insertion of a Notch with Different Radius in No Contact Simulations  
A notch was placed on the side of the specimen, as illustrated in Figure 2a, with different radii, as schematized in Figure 2b-e. The presence of a notch, as is the case of the crack, is a geometric discontinuity that acts as a stress concentrator. The objective of this section is to study the effect of the conjunction of the notch and crack on FCG, in the _no contact_ simulations. Figure 7a-f compare the development of \(\delta_{p}\) with \(\Delta a\) without contact, at the crack flanks, for different notch radii, \(r\) = 1, 2, 4, and 8 mm, for the three materials in study assuming both plane strain and plane stress states. The inclusion of the notch reduces the plastic CTOD range, and this effect increases with the radius. This means that the notch has a protective effect on \(\delta_{p}\) and therefore on da/dN, which results from a smoothing effect of stresses around crack tip. There is only one exception for the case of the AA6082-T6 in plane strain state, Figure 7c. The increase in \(r\) decreases \(\delta_{p}\), promoting a higher fatigue life as expected since stress-concentration factors decrease with the increase of \(r\). The protective  
Figure 5: Effect of contact of crack flanks on \(\delta_{p}\) versus \(\Delta a\) data (unnotched cracked specimen). (a) AA6082-T6; plane strain; (b) AA6082-T6; plane stress; (c) AA7050-T6 with pure kinematic behavior; plane strain; (d) AA7050-T6 with pure kinematic behavior; plane stress; (e) AA7050-T6 with pure isotropic behavior; plane strain; and (f) AA7050-T6 with pure isotropic behavior; plane stress. Figure 6: (a) Evolution of \(U^{*}\) with \(\Delta a\), for AA6082-T6 and AA7050-T6, with pure isotropic and kinematic hardening behaviors (unnotched-cracked specimen; contact); (b) Effect of \(U^{*}\) on CTOD vs. F curves (AA7050-T6 isotropic; unnotched-cracked specimen; plane stress). effect of the notch may sound strange. However, note that the crack length of the unnotched crack is 8.096 mm, as illustrated in Figure 8a. The protective effect of the notch is observed comparing the results of cracked geometries exhibited in Figure 8a,b. On the other hand, the comparison between cracked geometries in Figure 8b,c indicates that the notch accelerates da/dN, and this is the comparison typically made in literature. The dashed lines added to Figure 7, indicate the behavior expected for the cracked geometry of Figure 8c, i.e., assuming that the crack length is measured from the notch. As the crack becomes progressively longer, there is a global trend for the increase of \(\delta_{p}\) with \(\Delta a\), being the growth rate higher for lower values of \(\Delta a\). The effect of \(\Delta a\) is more pronounced for notched specimens than for unnotched specimens. These changes are due to the propagation of the crack tip through the stress field generated by the notch. For relatively large crack increments, the curves start to approach. This means that the notch is losing its effect and also that the difference between the curves is due to the notch. Anyway, for the maximum crack length studied \(\Delta a=1.272\) mm) the effect did not disappear totally because the curves still have some separation. This means that the effect of notch is larger than the 1.272 mm studied, particularly for the higher values of notch radius. On the other hand, for the smallest radius studied (\(r=1\) mm), the curves tend to the results of the unnotched specimens, which means that the boundary of the influence of notch was reached. Without contact at the crack flanks, the trends observed for \(\delta_{p}\) are not affected by stress state or material. Figure 9 plots \(\delta_{p}\) against \(r\) for three values of \(\Delta a\), in plane stress state and for the AA7050 with isotropic behavior. The increase of \(r\) and \(\Delta a\) reduces \(\delta_{p}\), as shown in Figure 7f.