**4. Conclusions**

In this paper, a methodology for the estimation of critical loads in tubular beams containing U-notches has been validated. The methodology is based on the application of the theory of critical distances (TCD) through the point method (PM) and finite element (FE) linear elastic simulations. The methodology has been validated in three Al6060-T66 cantilever beams containing circumferential through thickness U-notches, providing specific validation beyond that reported in fracture mechanics specimens.

Tensile and fracture tests allowed the corresponding material mechanical properties to be estimated, and the combination of fracture tests on notched SENB specimens and FE analyses allowed the material critical distance and inherent strength to be calibrated.

With all this, FE simulations of the notched cantilever beams were performed, determining the estimations of the critical loads (or load-bearing capacities) as those loads for which the PM criterion was fulfilled.

The predicted critical loads represent acceptable estimations of the experimental critical loads, almost within the typical accepted scatter band for fracture processes (± 20%), and with an average overestimation of + 5.7% (without any use of safety factors). The largest deviation (+ 20.4%) was observed in the beam developing the most evident nonlinear behavior, thus being further away from the initial linear elastic nature of the TCD, which makes it harder to compensate by the calibration process of the material critical distance.

The methodology may be applied to other structural components containing any kind of notches. However, further validation is required to establish general conclusions about its accuracy.

**Author Contributions:** Conceptualization, S.C.; methodology, S.C., M.S., B.A., and J.A.Á.; formal analysis, S.C and M.S.; investigation M.S., S.C., and B.A.; writing—original draft preparation, M.S.; writing—review and editing, M.S., S.C, B.A., and J.A.Á. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received funding from the Spanish Ministry of Science and Innovation, gran<sup>t</sup> PGC2018-095400-B-I00 "Comportamiento en fractura de materiales compuestos nano-reforzados con defectos tipo entalla".

**Conflicts of Interest:** The authors declare no conflict of interest.
