## 5 Conclusions  
The performed experimental and numerical studies revealed the following conclusions:  
1. The adhesive joint is the weakest link in the studied reinforced structures subjected to cyclic loadings.
2. The most frequent fatigue failure form was an adhesive failure between the steel and adhesive layer (S&P Resin 220, DP 6310 NS). In the case of the HY 4080 GY adhesive, failure occurred on both steel/adhesive and CFRP/adhesive interfaces.  
Figure 28: Comparison of 2-C acrylic, polyurethane and methacrylate adhesive properties.  
Damage mechanisms depend on the properties and components of the adhesives. In the performed fatigue tests, the fatigue life depended on the adhesive strength to substrates (to steel, in the case of S&P Resin 220 and DP 6310 NS; and to CFRP and steel, in the case of HY 4080 GY) and has a strong influence on the fatigue failure form.
4. The high-stiffness epoxy adhesive S&P Resin 220 exhibited a brittle damage mechanism. The damage in the adhesive layer was initiated immediately after the fatigue test began. After failure, an ultra-thin adhesive layer remained on the steel core, or complete debonding of steel was observed. Because of this, stiff and strong adhesives are not recommended for fatigue application.
5. In the case of polyurethane-based DP 6310 NS, the main failure form was an adhesive failure (including chipping, cracks and cohesive failure) between the steel and adhesive. The disadvantage of this adhesive is that it was less resistant to peel stresses under cyclic loading conditions.
6. Cyanoacrylate/Acrylic Hybrid Loctite HY4080 GY adhesive revealed the highest adhesion to steel. After the fatigue test, the adhesive retained its ductile behavior, but in the damaged areas, it was hardened. The highest fatigue life can be explained by resistance to peel stresses, a higher adhesion to substrates in vicinities of notches, the highest elongation at failure and the lowest tensile modulus.
7. It is recommended to apply adhesives with a small stiffness and relatively large elongation at failure. It is also very important to select adhesives that ensure the lowest possible peel stresses at the ends of overlays.  
The performed study revealed principal guidelines for the selection of adhesives for the reinforcement of notched steel structures by means of composite overlays working at cyclic loadings. Further experimental studies with a larger number of samples and loading conditions combinations will be carried out for soft adhesives with a high elongation at failure that were promising in the performed FEM analyses. However, there are still open questions about the formulation of theoretical approaches that can be used for the optimal selection of adhesives and assessment of the fatigue life of the adhesive joint. These can be made by the application of the methods based on the fracture mechanics or cohesive zone modeling.  
Conceptualization, P.J.R. and B.S.; methodology, P.J.R., B.S. and M.W.; samples preparation, M.W.; FEM analyses, B.S.; writing--original draft preparation, P.J.R., B.S. and M.W.; writing--review and editing, P.J.R. and B.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
This research was carried out with the support of the ANSYS National License coordinated by the Interdisciplinary Centre for Mathematical and Computational Modelling University of Warsaw, Poland (ICM UW). The publication presents results of the Project no 060/ZJE/2023/POT financed from the subsidy granted to the Cracow University of Economic.  
The authors declare no conflicts of interest.