## 1 Introduction  
Fatigue is one of the most common failure forms of structures and mechanical components subjected to cyclic loads. It is reported that such a process causes, in general, about 90% of failures of metal parts [1]. There are many factors that affect the fatigue strength and the fatigue life such as the stress ratio, type and frequency of loading changes and the environment; however, the greatest impact on fatigue life is the presence of notches and the type of notch and its size [2, 3]. The notch appearance, including openings [4], undercuts [5] and others, is usually an intentional human action, caused by constructional or technological reasons, and is unavoidable. In the vicinity of the notches, stress concentrations occur, which significantly reduce the fatigue life of the structure and its resistance to cracking. The sharper the notch, the greater the stress concentrations that occur, and these are also often accompanied by plastic strains [5], which, consequently, leads to lower fatigue strength and life. Therefore, the reinforcement of notched or partially damaged structures, which leads to a reduction in stress concentrations around the notch, is a popular method of increasing the fatigue life of a structure [6]. One of the methods that enables the reinforcing as well as repairing of damaged steel structures is the application of composite overlays. The reinforcing composite patches are most often installed by means of bonding [7, 8], riveted joints [9] and welded joints around the notch. Recently, it has been revealed that the application of adhesively bonded joints is a promising technique for the mounting of composite reinforcements [10, 11, 12]. The recently performed study [10] revealed that proper selection of the adhesive can increase the fatigue life of notched structure by even about 890%. However, there are no guidelines for the selection of adhesives for steel/composite joints. Such a lack of comprehensive reviews of the design of adhesive joints subjected to fatigue loadings is also mentioned in a recently published paper related to composite/composite bonded joints [13]. In the case of big structures, such a kind of reinforcement or retrofitting is usually cheaper than the elaboration of new ones and has recently become the standard practice in extending the lifetime of product. This way of designing is the contemporary trend of sustainable design and development, providing the minimization of costs. Such procedures are widely adopted in several branches of industry like aerospace, automotive, power engineering and other areas of mechanical and civil engineering. The extensive experimental studies [10, 14, 15, 16, 17, 18, 19] proved that the fatigue life of notched structures reinforced by the adhesive joint and composite patches can be significantly increased. Such an increase depends on different factors such as surface structure and the roughness of core and reinforcement materials, the treatment and preparation of elements of joint, the type of adhesive used, etc. Due to the more complex geometry, the fatigue behavior of the structures reinforced by adhesively bonded composite patches with the use of the adhesive joints is also much more complex in analyses than in the case of non-reinforced structural elements [20]. Except for the typical failure of substrates (composite patches or steel core), other forms of damage occur. These are adhesion failure (separation of the adhesive from composite or steel surface), cohesion failure (internal failure in the adhesive layer) and a mix of both adhesion and cohesion failure [6]. It is observed that the fatigue life of adhesive joints depends on many factors [21] such as, mainly, the manufacturing process and surface structure [13, 22], temperature, humidity [23], materials (adherents and adhesives) [24], the application of the pre-stress forces [25], etc. The review of the fatigue failure mechanisms of adhesive joints with a proposal of theoretical models for the analyses of typical adhesive joints is discussed by [PERSON] et al. [26].