*2.2. Circular Capillary—Influence of Diameter*

In this section, capillaries of circular cross section are considered. The influence of different diameter sizes on the stress field in the component is studied. In particular, as here above mentioned, one focuses on the axial stress in the initiation region (*S*11,*ini*) and on the capillary surface, as these are considered to be the best indicators of the influence the eSHM has on the initiation behavior. These results have been retrieved for five different diameters, namely 0.5 mm, 1 mm, 1.5 mm, 2 mm and 2.5 mm (respectively shown in brown, mauve, red, light blue and black on Figure 5a and on Figure 6), all being located so that the edge-to-edge distance "a" remains equal to 3 mm. These diameters corresponds to realistic values of what can be or will be achieved in a near future with the current or forthcoming additive manufacturing technologies. Indeed, technologies based on Powder Bed Fusion (PBF) have proven to be able to print capillaries down to 1 mm in diameter size, while technologies such as Direct Energy Deposition (DED) are currently limited to 2 mm. However, considering the evolution of the metal printing capabilities, and the advent of hybrid manufacturing, it is credible to think that smaller capillaries will be soon achievable. Therefore, it felt relevant to model capillaries as small as 0.5 mm in diameter, even if those are not yet printable.

**Figure 6.** Axial stress *S*<sup>11</sup> on the most critical line of the pin hole surface (bottom line in Figure 5, highlighted in orange), across the lug thickness, and as a function of the capillary diameter.

The axial stress values in the initiation region (cross-section bottom line in Figure 5) can be seen in Figure 6. As symmetry is used in the model, the results are presented for *z* = 0 mm to *z* = 2.5 mm, while the lug thickness is actually 5 mm. The reference lug experiences a maximum tensile axial stress of 336 MPa in the initiation region (also seen on Figure 3). On the graph of Figure 6, it can be seen that the presence of the capillary inside the lug raises the tensile axial stress level in that region, and therefore reduces the crack initiation life. However, it can be noticed that capillaries of very small dimensions (0.5 and 1 mm) have a very limited impact on the maximum stress level (339 MPa instead of 336 MPa). Table 1 summarizes this data, and also presents the maximum axial tensile stress on the capillary surface. It is noteworthy to realize that in all cases, the maximum stress on the capillary surface remains significantly inferior to the stress in the initiation region. This implies that in the case of a smooth capillary, a crack would normally not initiate at the capillary itself, as the lug hole surface remains the region where the amplitude of tensile stresses variations is the highest.

**Table 1.** Maximum axial tensile stress values in the initiation region (*S*11,*ini*) and on the capillary surface (*Smax*,*cap*) in function of capillary diameter (D). The results are compared with the reference lug, in which no capillary is integrated.

