*2.1. Numerical Framework*

The idea behind this research is to study the impact of the implementation of the eSHM technology in a potential practical application. Since the eSHM is originally targeted at aerospace applications, it has been decided to work on straight lug components. Indeed, this type of connecting element is frequently used in aeronautics, and is also very prone to fatigue failures (fretting and/or corrosion are very likely to initiate a crack) [28]. Amongst the abundant literature on lugs, it was decided to work on the configuration studied by Schijve in [29], where fatigue crack growth experiments have been performed on various aluminum straight lugs (in-plane geometry depicted in Figure 2, thickness of 5 mm) subject to a cyclically varying axial loading. The maximal pin force is *Fmax* = 21 kN and the load ratio is *R* = 0.33. It must be noted that this force is modeled through this entire work as an equivalent pressure having a cosinusoidal distribution on the pin hole surface. Moreover, even though a lug with integrated capillary would be barely impossible to manufacture without resorting to additive manufacturing, the material properties that are used in the present work are similar to the properties of the Al2024-T3 material used in the experimental work done in [29]. These are: a Young's modulus

of 73,000 MPa, a Poisson's ratio of 0.33, and a yield stress of 368 MPa. It is thus assumed that the material is isotropic, and that the variations of the mechanical properties due to the printing process do not influence the results of the comparison provided the same material properties are enforced in all the models.

**Figure 2.** Dimensions (in mm) of the lug modeled, and pin loading modeled as an equivalent pressure with cosine distribution around the hole.

Figure 3 shows the axial stress field *σxx* (the *x*-axis is along the longitudinal direction, as shown on Figure 2), further noted as *S*11, on the lug when subject to the maximal axial pin loading. The highest tensile stresses are found on the top and bottom regions of the pin hole surface and reach 336 MPa (effectively corresponding to a stress concentration factor of 2.8 with respect to the maximum net tension stress, see [29]). Excluding manufacturing defects, the highest probability of crack initiation is thus also found there. These two regions of high tensile stresses will hence further be referred as the "initiation regions" and are the focus in this part of the study. It must be noted that, considering this stress distribution, capillaries should be placed and limited to the neighborhood of these initiation regions. However, in an actual practical application, the loading could have a non-axial component. Moreover, in testings, notches are introduced in these area's in order to trigger initiation at a known place, which is of course not done in an operational component. As a consequence, the initiation region is never as clearly defined as what has been assumed here. Therefore, capillaries are integrated all around the hole of the studied lug, so as to enable detection of any crack that initiated at the hole surface (see Figure 4).

**Figure 3.** *S*<sup>11</sup> field on the lug, highlighting the most probable region for initiation under cyclic and purely axial loading.

**Figure 4.** Cut views of the lug equipped with eSHM on a XY plane at mid-thickness (**a**) and on a YZ plane centered at the lug hole (**b**). The capillary around the hole is clearly visible (in the shown topology, the capillary is circular with a diameter of 2 mm).

While the eSHM system has the advantage of a very simple principle of operation, conferring a significant robustness to the system, and since the parts equipped with eSHM have to be manufactured by additive manufacturing, it still presents a considerable design freedom in terms of engineering. Indeed, the capillary shape is in principle arbitrary and can be "chosen" by the designer, as well as its dimensions. However, keeping in mind that one should avoid salient edges and convex shapes, this design freedom is restrained and one will limit oneself to capillaries of circular and elliptical cross section. Nevertheless, the diameter/aspect ratio of the capillary can be tuned, and this part of the study aims at quantifying in which proportion the capillary diameter/aspect ratio influences the crack initiation behavior. Besides, the "edge-to-edge" distance between the bottom of the capillary and the lug hole surface, referred here as distance "a" (in accordance with the terminology used in the works [6,26,27]), is also a parameter in the engineering of the crack detection system. A smaller edge-to-edge distance would imply a quicker detection of the propagating crack, and again, one aims at quantifying the influence of this design parameter on the crack initiation. It must be noted that the pressure inside the capillary also is another design parameter, but it has been shown in a previous study that, at the pressurization levels used, no effect was observable on the stress field in the component [14].

The parametric study led in this work therefore concentrates on the influence of capillary shape (circular or elliptical), dimension (diameter and aspect ratio), and edge-to-edge distance with respect to the monitored region (lug hole surface). Figure 5 illustrates the different configurations under consideration. Static simulations of the different configurations subject to the maximum pin loading (*Fmax* = 21, 000 N) have been run, and the resulting maximum tensile stresses on the lug hole surface and capillary surface are compared to the situation of a "standard" or "reference" lug where no capillary has been integrated. For the sake of accuracy of the numerical results, one has taken advantage of the symmetry of the problem and only a quarter of the lug has been modeled. The mesh, consisting of about 700k (exact number depending on the eSHM configuration) linear hexahedron elements, has been obtained after several refinement steps to ensure the use of a converged mesh.

**Figure 5.** Schematics of the upper cross section of the lug when looking in a YZ plane centered at the lug hole (one can refer to Figure 4b), illustrating the different implementations of the eSHM (capillaries) that have been assessed. In particular, different capillary diameters (**a**), edge-to-edge distance (**b**) and aspect ratio's (**c**).
