**3. Results**

The main tensile properties of the Al6060-T66 being used are gathered in Table 3, with *E* being the Young's modulus, σ*0.2* being the proof strength, σ*u* being the ultimate tensile strength, and ε*max* being the strain under maximum load.


**Table 3.** Mechanical properties (mean and standard deviation).

Table 4 presents the experimental results of the fracture tests, with Figure 8 showing some representative examples of the experimental load–displacement curves obtained for each notch radius. Here, it is important to notice that the fracture resistance values obtained are high, even in cracked conditions. In this sense, Equation (3) provides a criterion to estimate the onset of the plane stress conditions [19], with *B* being the thickness and <sup>σ</sup>*y* being the yield stress (the proof stress for the material being analyzed here). It is straightforward to derive that plane stress conditions are achieved for fracture resistance values above 26.7 MPam1/2, approximately, so all the SENB specimens being tested are under plane stress conditions, explaining the high values of fracture resistance obtained here. This is also important to justify the scarce influence of the election of the tube selected for tensile and fracture characterization. As long as the two possible thicknesses (5 mm vs. 6 mm) generate fully plane stress conditions, the influence of this dimension on the resulting fracture resistance may be considered to be negligible.

$$K\_{\text{Plame Stress}} = \sigma\_Y(\pi B)^{1/2} \tag{3}$$


**Table 4.** Experimental results obtained in SENB specimens. *KNmat* in cracked specimens correspond to the material fracture toughness *Kmat*.

**Figure 8.** Load–displacement curves of some of the fracture tests.

The load–displacement curves of the structural tests performed on the notched cantilever beams are shown in Figure 9, while the corresponding values of the critical load (in terms of the experimental load-bearing capacity, LBCexp) are presented in Table 5.

**Figure 9.** Load–displacement curves of the different tubular beam.


**Table 5.** Values of *L* and σ*o* obtained from calibration, together with the experimental and the estimated values of load-bearing capacity (LBC).

Concerning the FE simulations, the stress–distance curves obtained in the fracture section of the SENB specimens are shown in Figure 10. When the PM is applied in more than two geometries, and the number of tests is limited, it can be observed that the di fferent curves do not necessarily cross each other at the same point, as shown in Figure 6. Following the PM, and considering the inherent scatter of fracture processes, a much larger number of specimens per notch radius would be needed to obtain a single crossing point. For this reason, the material parameters, gathered in Table 5, have been obtained in this work as the average of the di fferent cuto ff points, the essential assumption of the PM being reasonably fulfilled. Analogously, Figure 11 shows the stress–distance curves corresponding to the di fferent tubular beams when a load of 1 N is applied in the free edge.

**Figure 10.** Stress–distance curves at critical load in SENB specimens. The solid circles correspond to the cuto ff points.

**Figure 11.** Stress–distance curves in tubular beams when applying a unit load (1 N) at the free end.

Once the experimental results and the FE modeling have been presented, Table 5 also shows the estimations of the load-bearing capacity (LBCest) for each tube.

Figure 12 compares the experimental results and the corresponding TCD-FE estimations, showing acceptable predictions of the load-bearing capacity. All the results are basically in the ±20% scatter band, which is generally accepted in fracture research [19,28–30], with an average overestimation of the LBC of +5.7%. This is also understandable, taking into consideration that this approach does not include any safety factor, something commonly used in structural integrity assessments. It can be noticed that the maximum deviation (+20%) occurs in the tube with the largest notch radii (ρ = 1.5 mm), which has the more pronounced nonlinear behavior (see Figure 9). It seems that although the TCD compensates nonlinearities with the calibration process (through σ0 values larger than <sup>σ</sup>*u*), the resulting LBC estimations may lose accuracy when the material's nonlinear behavior becomes more developed.

**Figure 12.** Comparison between the experimental results (LBCexp) and the resulting estimations (LBCest).
