*2.3. Circular Capillary—Influence of Edge-to-Edge Distance*

Bringing the capillary closer to the initiation region (thus, reducing the distance "a") is desirable for earlier detection of fatigue cracks that would develop at the lug hole surface. However, the influence it has on stress raise in the initiation region and at the capillary surface has to be studied. In the experimental investigations around the eSHM, the distance "a" is traditionally set to 2 mm [26,27]. Therefore, for the purpose of this parametric study, the diameter of the capillary was kept constant at 1.5 mm, and edge-to-edge distances equal to 3 mm, 2 mm and 1 mm have been considered (respectively shown in red, black and green on Figure 5b).

The results are presented in Table 2. These demonstrate that earlier crack detection (smaller "a" distance) inherently comes with a raised stress level in the initiation region, but this raising remains very limited (increase of 1.9% between *a* = 3 mm and *a* = 1 mm). Moreover, even for an edge-to-edge distance of 1 mm, the tensile stress level on the capillary surface remains inferior to the tensile stress level in the initiation region. Again, this implies that the lug hole surface would remain the initiation site. It is however noteworthy to realize that in practice, due to the current limitations in additive manufacturing technologies, the roughness level in the capillary acts as a significant stress raiser, and implies that when brought too close to the surface, cracks actually initiate at the capillary instead of at the surface. This has been thoroughly studied in the work by Günther et al. [22]. This is also the reason why experimental testing around the eSHM has traditionally used an edge-to-edge distance of 2 mm [26,27]. From this, it can be inferred that capillary roughness is the main challenge to the practical implementation of the eSHM, as the presence of the capillary itself should not affect the crack initiation site nor significantly the crack initiation life, provided the capillaries are small with respect to the lug dimensions.


**Table 2.** Maximum axial tensile stress values in the initiation region (*S*11,*ini*) and on the capillary surface (*Smax*,*cap*) in function of edge-to-edge distance (a).
