*3.2. Influence of Capillary Diameter on Crack Growth Life*

In what follows, the "crack length" refers to the distance between the lug hole surface and the intersection between the crack front and the side surface of the lug. This choice has almost no influence on the crack growth curve of the part-through crack since the crack front curvature is very limited. However, concerning the quarter-elliptical crack, this definition implies that the number of cycles to detection (corresponding to the moment where the crack breaches the capillary) does not correspond to a crack length equal to 3 mm (see Figure 8).

The crack growth curves are presented in Figures 9 and 10. The number of cycles to failure and number of cycles to detection are given respectively in Tables 4 and 5. It is interesting to note that even though a simple crack propagation model has been used, the fatigue life obtained for the reference lug and for the part-through crack, namely 11,470 cycles, agrees fairly with the experimental works of Schijve, where the fatigue life of the specimens oscillated between 13,500 and 15,500 cycles [29]. For the quarter-elliptical initial defect, the numerical results cannot really be compared to the experimental works of Schijve, as the initial defect introduced in the experiment (a corner crack) is different than the one modeled in the present research.

**Figure 8.** Crack front just before reaching the capillary (2 mm diameter) after propagation of the initial quarter-elliptical defect.

**Table 4.** Fatigue crack growth lives (*Nf*) and cycles to detection (*Nd*) as a function of capillary diameter, in the case of part-through crack. The variation of fatigue life compared to the reference lug (Δ) is also given, as well as the Remaining Useful Lifetime after detection (*RULd*).


**Table 5.** Fatigue crack growth lives (*Nf*), variation with respect to the reference lug (Δ), cycles to detection (*Nd*) and post-detection Remaining Useful Lifetime (*RULd*) as a function of capillary diameter and in the case of quarter-elliptical crack.


Several interesting observations can be made from these crack propagation computations. First, for both types of defects, small capillaries have a limited negative impact in terms of the fatigue crack growth lifes. The impact that would be tolerated by a component manufacturer would inevitably be application dependent. However, to set ideas, one considers here that a reduction by 5% of the crack growth life compared to a reference lug remains acceptable. With this assumption, capillaries of 0.5 mm and 1 mm are acceptable designs. Conversely, for large capillaries, the severe stress state on the propagation plane implies that the stress intensity factor field on the crack front is also more severe. In the first propagation step computed, the maximum mode I stress intensity factor on the reference lug for a part-through crack is 586 MPa√*mm*, while it already reaches 644 MPa√*mm* for the lug equipped with a 2.5 mm diameter capillary. The propagation speeds are thus already larger, even before the crack reaches the capillary. This is clearly seen on Figure 9. Second, it is worth noting that this trend is consistent with the effect capillaries have in terms of crack initiation. This illustrates the interest of working with relatively small capillaries (compared to the dimensions of the component), which is also the direction aimed for in the research around the eSHM methodology. Third, for the part-through

crack, the detection occurs early in the crack propagation life, and can be further improved, should it be needed, by bringing the capillary closer to the initiation region. Indeed, as shown in Table 4 and in Figure 9, the remaining post-detection crack growth life represents 60% of the total crack propagation life (*Nf*). However, due to the lower propagation rates in the early stage (clearly seen in Figure 10), this is not true anymore for the quarter-elliptical crack. Indeed, the Remaining Useful Lifetime after detection is reduced in this case to barely 30% of *Nf* . Therefore, alternative designs, such as integrating two ex-centered capillaries, could be envisaged to remedy this when needed. Finally, it must be noted that the presence of the capillary has no influence on the crack path, which is in all cases straight in the *y*-direction.

**Figure 9.** Fatigue crack growth curves for various capillary diameters, for a part-through crack.

**Figure 10.** Fatigue crack growth curves for various capillary diameters, for a for a quarter-elliptical crack.
