Fracture Mechanism of Adhesive Layers in Fatigue-Loaded Steel Structures Reinforced by the CFRP Overlays

Abstract

The behavior of the adhesive layer has a strong influence on the fatigue strength and life of the adhesively bonded structures. This phenomenon is of particular importance in the case of bonding of different materials like metals and composites. In such a case, the different mechanical properties of the adhesive layer have a crucial influence on failure resistance. In particular, adhesions to both materials, the tensile modulus, shear strength and the maximal elongation are of the main importance. The influence of the mechanical properties of the adhesive layer on the fatigue life of steel/composite adhesively bonded structures is presented in the paper. The additional factor influencing the fatigue life of structural elements is the presence of notches. In order to take into account both factors, a notched steel sample reinforced by the composite overlays is used. The numerical calculations were performed for several different adhesives. In the experimental analyses, three adhesives composed of different ingredients and with different mechanical properties have been investigated. The study is focused on the failure mechanisms of the adhesive layers. The highest fatigue life has been obtained for the adhesive that exhibits the largest maximal elongation and the smallest tensile modulus and provides the best adhesion to the steel core. Finally, the guidelines for the choice of the most effective adhesive were proposed based on the fracture mechanisms of the adhesive layers observed in the experiment and the results of the performed numerical analyses.

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 (adherends 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 Yao et al. [26]. It is recommended to use the linear elastic fracture mechanics or the traditional damage mechanics for hard adhesives (with high tensile modulus). In the case of soft adhesives, in which high energy dissipation and large deformation may occur, a cohesive zone model can be used [27].

Many scientists investigated the problem of the repairing and reinforcing of notched metal structures by composite overlays with the aim of increasing fatigue strength and life. One of the weakest parts of adhesive joints is the adhesive interface [28]. Many works consider the influence of the stiffness of the system core/overlays on the distribution of stresses in the adhesive interface [6]. However, only limited studies are focused on the analyses of the fracture mechanisms of adhesive joints subjected to fatigue loadings.

The important conclusions, however, obtained only for static loading conditions, were provided by Wu et al. [29] and Li et al. [30]. Wu et al. [29] observed that the application of more ductile adhesives (Araldite 420) leads to more uniform and smaller shear stresses in the adhesive interface. On the other hand, the application of less ductile and stiffer and stronger adhesive (Sikadur 30) resulted only in the cohesive failure of the interface. The comparison of different adhesives under static loading conditions was carried out by Li et al. [30] and they observed that the failure mode depends on the mechanical properties of the adhesive. In contradiction to the results shown by Wu et al. [29], they obtained cohesive failure for the adhesive with the largest stiffness (Sika 30—Elastic modulus 12 GPa).

Lepretre et al. [31] investigated cracked steel structures reinforced by CFRP laminates and observed that the largest increase in fatigue life was obtained for double-side reinforcement. The authors observed cohesive failure in the adhesive layer when normal modulus CFRP (165 GPa) was applied, and mixed-mode damage (CFRP rupture and delamination) in the case of the application of CFRP with an ultra-high modulus (460 GPa). A similar reinforcement technique was applied by Liu et al. [32]. They observed two different failure mechanisms—composite failure (when patches with high a CFRP modulus of 640 GPa were applied; the increase in fatigue life was 4.7–7.9 times) and interfacial debonding (a normal CFRP modulus of 240 GPa overlays was used; the increase in fatigue life was 2.2–2.7 times). They also noted that bond width is a significant parameter in the context of fatigue life. The problems of interfacial debonding can be investigated with the use of finite element methods (FEM) and fracture mechanics (i.e., mixed-mode cohesive law) [21,33].

Studies of steel specimens with cracks reinforced by CFRP with the use of epoxy resin adhesive were performed by Yu et al. [34], in which debonding failure was spotted (the increase in fatigue life was 97–186%).

The experimental tests for aluminum specimens with circular holes and reinforced by CFRP multilayered patches and with the use of Sikadur 330CN adhesive were studied by Wang et al. [18]. The typical observed failure form was the interfacial debonding and the increase of the fatigue life was in the range of 25–69%. Similar studies and results were also reported by Wang et al. [15] for steel specimens with circular holes in which interfacial debonding occurred at the steel/adhesive interface. The studies concluded that insufficient composite thickness with respect to the core stiffness causes excessive loading of the adhesive interface and leads to adhesive and reinforcement failure. The fatigue tests with the use of different steels reinforced by CFRP overlays glued by E2500S resin were carried out by Hu et al. [35] (the increase in fatigue life was 1.3–3.1 times). They observed different contributions of mixed-mode failure (delamination and debonding) dependent on the applied stress level and steel. A series of studies of different FRPs and several adhesives have been performed for structural elements including various types of cracks [17,31,32,34,35,36,37]. Again, the application of FRP reinforcements has proved its robustness. Not only separate and common applications of FRP reinforcements were under investigation. Here, the examples are structures or structural elements where bolted connections also appear beside the adhesively bonded overlays [14,38].

Despite certain guidelines for the design of adhesive reinforcement for fatigue application, there is still a lack of knowledge related to the studies of the fatigue behavior of the adhesive interface [13]. In the available fatigue studies, the influence of some parameters such as the stiffness of CFRP patches and their geometry, number, position of overlays, etc. have been studied. The previously reported results of the fatigue tests [10] revealed that the adhesive has a key influence on the reinforcement effect. Recently, some guidelines for the design of adhesive joints for composite–composite structures have been proposed. It has been observed that the fatigue life of the adhesive joint can be increased by, i.e., incorporating additive particles [39], hybridization of the joint [40] or hygrothermal pre-conditioning [41]. However, there are no comparative studies in which different adhesives were tested under the same cyclic loading conditions. There are some studies referred to static loading conditions, but these results cannot be transferred and extended to fatigue problems. To the best knowledge of the authors, no further investigations have been made in the context of the above-mentioned issues. Based on the above insights, the novelty and the main aim of the proposed study is to formulate the guidelines for the selection of the adhesives for reinforcements of steel structures by CFRP overlays working at cyclic loading conditions. This is made by comparison of the detailed analyses and comparison of failure mechanisms (of steel core and adhesive layer) of the same structures and subjected to the same loading conditions but with different adhesives applied.

In the vast majority of publications devoted to research on notched steel elements reinforced with composite overlays and subjected to periodic loads, only moderate values and variations of fatigue loadings are applied [6,7,8,9,11,14,15,16,17,18,20,28,29,30,31,32,34,35,36,37,38]. The novelty of the proposed paper relies on investigations of the failure forms of adhesive bonds subjected to extreme fatigue loadings. Here, in the performed test, the sinusoidal form of the loading cycle with stress ratio R = 0.1 and maximum tension load F equivalent to 90% of the yield limit is applied. Due to the presence of the notch, in the investigated sample zones with plastic deformations are present for such a force, which, additionally, makes the analyses difficult and complicated. These are very tough fatigue-loading conditions, which are not common and addressed in the published papers [6,7,8,9,11,14,15,16,17,18,20,28,29,30,31,32,34,35,36,37,38]. Such a kind of loading is rather characteristic of highly stressed structures in mechanical appliances. In the performed failure-form analyses, particular attention is paid to the failure forms of different adhesives used and the influence of their technical data on the form of adhesive disintegration.

There are many adhesives available on the market. Due to missing guidelines for the selection of adhesive for the reinforcement of steel structures by CFRP overlays, in the paper, the experimental study is performed using three chemically different kinds of adhesives. These are the two-component adhesives prepared on the chemical base of epoxy resin, polyurethane and cyanoacrylate/acrylic. Additionally, the chosen adhesives differ in the Young’s modulus value from relatively hard epoxy resin to the remaining two mild adhesives. Such a choice may be considered as the introductory one and should be developed in further experimental studies. This study focuses on assessing the mechanism of adhesive joint degradation and determining the key factors and parameters of adhesives affecting fatigue strength. For this reason, the additional numerical analyses for a larger group of adhesives were carried out. Finally, on the basis of the experimental results and several comparative simulations, a certain methodology for the choice of adhesives is proposed for the periodically highly loaded structural elements with notches. These particularly refer to the metallic structures.

The paper consists of five sections. The introduction, including the literature review, is given in Section 1. The methodology, materials and finite element method (FEM) models are described in Section 2. The results of the experimental studies and numerical analyses are presented in Section 3. A discussion of the obtained results is given in Section 4, and finally, conclusions are provided in Section 5.

2. Materials and Methods

The experimental fatigue tests were carried out on notched steel samples reinforced by adhesively bonded CFRP stripes (Figure 1). The core of each sample was made of low-alloy and normalized S355J2+N low-carbon manganese structural steel (ArcelorMittal Poland S.A. Oddział w Krakowie, Kraków, Poland) with chemical composition as follows (in weight %): C, 0.15; Si, 0.13; Mn, 1.33; Al, 0.04; Cu, 0.02; P, 0.01; S, 0.04; Fe, res. The tested steel exhibited the following mechanical properties: Young’s modulus, 210 GPa; Yield strength Ye, 427 MPa (±11 MPa) and ultimate tensile strength, 528 MPa (±10 MPa); elongation at failure (A₅), min 22%. Its tensile curve is characterized by a typical stress–strain curve for mild steels including the yield plateau (plastic flow), strain hardening and necking [10]. The notch in the form of a square hole with rounded corners (radius R2) in the core was cut by using laser cutting technology. The CFRP stripes were made of prefabricated S&P C-laminate 150/2000 (S&P Reinforcement Poland, Malbork, Poland) with a main elastic modulus of 165 GPa, ultimate tensile strength of 2800 MPa, fiber volume content not less than 68%, density 1.6 g/cm³ and elongation at break not less than 16% [42]. The thickness of the single strip was equal to 1.4 mm. The strips were glued on the steel core so that the fibers were arranged parallel to the direction of the tensile force (parallel to direction of x-axis in Figure 1b). Such strips were attached by means of an adhesive joint.

Finally, the experimental fatigue tests have been performed for notched steel samples reinforced with the use of three different adhesives (Figure 1):

• Solvent-free, thixotropic, two-component epoxy resin adhesive S&P Resin 220 (S&P Reinforcement Poland, Malbork, Poland)—4 samples tested;
• Two-component polyurethane-based structural adhesive 3M Scotch-Weld DP 6310 NS (3M Poland Sp. z o.o., Kajetany, Poland) —3 samples tested;
• Two-component structural hybrid Cyanoacrylate/Acrylic Hybrid Loctite HY 4080 GY (Henkel Polska Sp. z o.o., Warszawa, Poland)—3 samples tested.

The principal properties of the adhesives are given in

Table 1. Mechanical properties of adhesives tested experimentally.

Adhesive	Structure	Tensile Modulus (MPa)	Shear Strength (MPa)		Tensile Strength (MPa)	Maximal Elongation (%)
			Steel 1	CFRP
S&P Resin 220	2C Epoxy	7000	26	26	14.0	1
DP 6310 NS	2C Polyurethane	544	13	22	18.0	54
HY 4080 GY	2C Cyanoacrylate/Acrylic	355	25	n.a. 2	11.3	80

¹ Cold rolled steel/mild steel. ² n.a.—not available. Data are not provided by the manufacturer.

. Before the bonding procedure, the steps suggested by the glue manufacturer have been carried out. The steel adherents were grounded in order to remove surface defects and oxide layers. In the next step after that, the sample surface was cleaned with extracted gasoline, sanded and, again, cleaned before bonding the CFRP overlays. A more detailed description of the sample preparation and the results of the fatigue tests are given in Ref. [10]. For each of the adhesives, at least three fatigue tests were carried out. The samples were subjected to tensile load with stress ratio R = 0.1 and with the maximal force Fmax = 47.5 kN, which is equal to 0.93 Ye.

2.1. FEM Model

The detailed numerical calculations of the investigated samples were carried out with the use of the ANSYS Finite Element Method Software ver. 2022R2 (ANSYS Inc., Canonsburg, PA, USA) [43], which is one of the leading codes in these subjects. As it was mentioned above, all studied samples are composed of three different materials, namely, steel core and four reinforcing overlays attached to the metal part by means of the respective adhesive layers. Due to the structure composition—the relation of thicknesses to the remaining dimensions of the respective components—both 2D or 3D models can be introduced [44]. However, the application of the 3D model brings more valuable results and enables the user to thoroughly assess the strains and stress distributions in all elements (see Figure 2). Three different materials are distinguished by means of three different colors. In Figure 2, the cyan color stands for the steel core, red is equivalent to the adhesive and violet is reserved for the CFRP overlays. In this particular case, the SOLID185 finite elements were used. It is, in general, defined by eight nodes having three nodal displacements $(u,v,w)$ as the degrees of freedom. Such finite elements are suitable for the analysis of problems with plasticity, hyper-elasticity, creep, large strains and large deflections, which can be observed in hybrid structural elements under investigation. Additionally, it has also capabilities adequate for analysis of the behavior of nearly incompressible or even fully incompressible hyper-elastic materials and orthotropic materials. The main difficulty in the modeled sample is caused by the presence of sharp corners in the position when the shape of the opening hole transforms from straight to curvilinear one. This just appears in the close vicinity of the bonded overlays. This is, in fact, the notch area and a relatively high density of the finite elements mesh is demanded for the proper mapping of the stress gradient distribution. In these areas, the strong distortion of the finite elements modeling the structure is expected. Fortunately, the applied finite element allows for certain element shape degeneration without the meaningful loss of the solution accuracy. Here, in the notch area, very small prism-shape solid finite elements are generated. Also, outside the notch in the steel core, a division of the notch close sub-volumes was proposed that provides an almost regular mesh of the generated elements. The detail of the proposed mesh shape in the described area is shown in Figure 3. Due to the symmetry of geometry and loadings, even one quarter of the sample may be investigated. Here, detailed calculations were performed for the symmetric half of the structure. Such a model enables the introduction of variable bond thickness not only on the top and bottom sides of the steel core (when ¼ is modeled) but also on both sides of the opening in future calculations. As a result, the size of the investigated model increases but usage in calculations of the computer with four processors and a relatively large amount of RAM memory results in a reasonable calculation time for the model with approximately 1.5 million active degrees of freedom.

As can be seen in Figure 3 across the steel core thickness, eight FE element layers were applied; three finite elements were used for each adhesive layer, while five elements were applied across the height for the top and bottom overlays. The proposed finite element mesh was slightly improved from the one applied in the paper [10] and successfully verified by experimental measurements with the use of digital image correlation [45]. The exemplary comparison of measured strains (DIC) with strains calculated by FEM model are shown in Figure 3b. The paths and x-axis are defined in Figure 1b. It can be seen that the obtained results are quantitatively and qualitatively consistent. It should be mentioned here that it is assumed that the real structure and the studied numerical model does not include defects like uneven thickness of the adhesive, porosity or other voids and faults. It is also assumed that no cracks are appearing in the sample. Due to the fact that the applied external force is so high (47,500 N), the material model used for the steel core should also model elastoplastic properties. Here, the real nonlinear, true stress–strain curve was used in calculations [10], including the kinematic hardening plastic mechanism being taken into account.

Different adhesives were investigated in the numerical study. Generally, adhesives consist of two or more components in which the main component is based on cyanoacrylate/acrylic hybrid, epoxy or polyurethane substrates. The following aspects were taken into account in the selection process of the adhesives listed in

Table 2. Mechanical properties of adhesives tested numerically.

Designation	Metal Composites Plastics	Structure	Tensile Modulus (MPa)	Shear Strength (MPa)		Tensile Strength (MPa)	Maximal Elongation (%)
				Steel	CFRP
Araldite 2011	MCP	2C Epoxy	1900	25	19	24	9
Araldite 2012	MC	2C Epoxy	2500	21	14	44	4
Araldite 2014-2	MC	2C Epoxy	3100	20	17	30	1
Araldite 2015-1	MC	2C Epoxy	1600	23	22	31	4
Araldite 2019	MCP	2C Epoxy	1600	27	35	40	4.3
Araldite 2031-1	MC	2C Epoxy	1000	24	20	23	12
Araldite 2048-1	MCP	2C methacrylate	364	19	23	13	91
Araldite 2051	MCP	2C Acrylic	1700	25	18	40	10
Araldite 2053-05	MCP	2C Acrylic	1000	21	27	15	50
Araldite 2053-15	MCP	2C Acrylic	1000	21	22	19	60
Araldite AW4858	MCP	2C Epoxy	1600	26	41	31	7
Sikadur 30	MC concrete	2C Epoxy	11,200	16	16	26	<1
SikaPower 1277	MC	Epoxy	2000	28	28	30	4
SikaPower 1548	MCP	2C Epoxy	1000	26	26	26	12
SikaForce 7720 L45 (420 L45)	MCP	2C polyurethane	100	10	10	12	33
SikaForce 7888 L10	MCP	2C polyurethane	1500	20	20	30	40
SikaFast 5221 NT	MCP	2C Acrylic	250	10	10	10	200
Plexus 420	MCP	2C methacrylate	1000	15	23	17	20
SG300 series (-05, -15, -40)	MCP	2C methacrylate	207	16	16	12	40

: manufacturer recommendations about adhesive application, bonding materials, recent application and mechanical properties. Most of the listed adhesives are commonly used in aerospace applications. The mechanical properties of composite overlays (T700/QY9511) used in the FE analyses of the adhesives listed in Table 2 are as follows: E₁₁ = 130 GPa, E₂₂ = E₃₃ = 10.4 GPa, G₁₂ = G₁₃ = 6.36 GPa, G₂₃ = 4 GPa, ν₁₂ = ν₁₃ = 0.3 and ν₂₃ = 0.41 [46]

3. Results

3.1. Influence of Adhesive on Fatigue Life

The square hole acts as a notch and results in severe stress concentrations in the vicinity of the hole. This results in the occurrence of plastic deformations in these areas due to the cyclic loading and results in crack initiation and propagation. The application of the CFRP reinforcement leads to a reduction in the stress concentrations and results in the delay of the crack initiation and slowing down after its initiation. In both cases, the influence of the notch on the crack growth is typical and described in the literature [1,2]. The observed forms of fatigue failure of steel cores for bare and reinforced samples differ in the size of necking; the largest one is observed for the bare steel sample and is getting smaller and smaller while using S&P Laminate, DP6310NS and HY 4080GY adhesives, respectively. What is more, for the HY 4080GY, at least at one side, the necking does not appear. Application of the CFRP overlays evidently increases the fatigue life of the investigated samples’ endurance to varying degrees [10]. The beneficial effect of the reinforcement is in taking over part of the external load and, consequently, reducing the stress concentration in the corners of the holes.

The performed fatigue tests [10] revealed that the fatigue life of steel/CFRP adhesive joints strongly depends on the adhesive type. The fatigue life increase ($FLI$) was calculated as a relative change between the fatigue life of the reinforced sample $N_{f,avg}^{reinf}$ and the fatigue life of the bare sample (without adhesive joint) $N_{f,avg}^{bare}$ as follows:

$$FLI\left(\%\right)={\displaystyle \frac{N_{f,avg}^{reinf}-N_{f,avg}^{bare}}{N_{f,avg}^{bare}}}100\%.$$

(1)

The highest fatigue life was obtained for samples in which HY 4080 GY cyanoacrylate/acrylic adhesive was used (Table 2). In this case, the average increase in fatigue life was equal to $FLI$ = 890%. The application of the DP6310NS polyurethane adhesive also leads to a considerable increment in fatigue life ($FLI$ = 307%). The lowest fatigue life ($FLI$ = 97%) occurred in samples in which S&P Resin 220 epoxy resin was applied. In all cases of reinforced samples, their fatigue life was at least two times greater than the fatigue life of the bare (not reinforced) samples. Additionally, stress concentration factors Kt (elastic analyses) are listed in

Table 3. Fatigue life of tested samples. SD—standard deviation.

Adhesive	$\mathbf{Average} \mathbf{Fatigue} \mathbf{Life} {\mathit{N}}_{\mathit{f},\mathit{a}\mathit{v}\mathit{g}}$ (Cycles)	Average Fatigue Life Increase FLI (%)	Stress Concentration Factor
Bare sample (without CFRP stripes)	37,926 (SD: 605 cycles)	Not valid	2.669
S&P Resin 220	74,613 (SD: 17 × 103 cycles)	97	1.725
DP 6310 NS	154,471 (SD: 15.5 × 103 cycles)	307	1.853
HY 4080 GY	375,462 (SD: 49.8 × 103 cycles)	890	1.852

. It can be seen that there is no relationship between Kt and the increase in the fatigue life of the reinforced structures. The lowest fatigue life was obtained for S&P Resin 220, for which the lowest Kt occurred. Therefore, the properties of adhesives are crucial for fatigue life.

3.2. Failure Forms of Steel/Composite Adhesive Joints

The investigated adhesive joints consist of three elements—the steel core, composite overlays (adherends) and adhesive layer. Such a structure undergoes a complex form of failure form (Figure 4). The most commonly observed failure forms are adhesive failure (Figure 4a), cohesive failure (Figure 4b), failure caused by peel stresses (at the end of the adhesive joint—Figure 4d,e) and adherend failure (Figure 4f). The most dominant failure form in the performed experiments was the adhesive failure (Figure 4a). Generally, the weakest point in the performed experimental tests was the adhesive connection with the steel surface.

3.3. Preliminary Comparison of Mechanical Behavior of Adhesive Joints

The samples were subjected to tensile load, which, in the case of the bare samples, results in nominal stresses equal to about 0.93 of the yield limit of the tested steel. Moreover, due to the occurrence of the notch, the stress concentration factor was about 2.48 (theoretical) to 2.67 (numerical 3D) [10]. In such a case, cyclic loading resulted in the formation and development of large plastic zones in the weakened part of the sample. In order to compare the fatigue behavior of the different adhesives applied, the following normalized stiffness parameter $R$ was used:

$$R(n)={\displaystyle \frac{R_n\left(n\right)}{R_0(n=1000)}}={\displaystyle \frac{\frac{F_{n,\mathrm{m}\mathrm{a}\mathrm{x}}-F_{n,\mathrm{m}\mathrm{i}\mathrm{n}}}{u_{n,\mathrm{m}\mathrm{a}\mathrm{x}}-u_{n,\mathrm{m}\mathrm{i}\mathrm{n}}}}{\frac{F_{n=1000,\mathrm{m}\mathrm{a}\mathrm{x}}-F_{n=1000,\mathrm{m}\mathrm{i}\mathrm{n}}}{u_{n=1000,\mathrm{m}\mathrm{a}\mathrm{x}}-u_{n=1000,\mathrm{m}\mathrm{i}\mathrm{n}}}}}.$$

(2)

Here, $u_n$ and $F_n$ mean corresponding displacements and applied forces in the n-th cycle. The normalized stiffness ($R_0$) was determined for n = 1000 cycles for each sample. The above parameter ($R)$ allows the visualization of occurring damage during the fatigue process. The initial value of the normalized stiffness is obviously equal to 1. Its reduction indicates the occurrence of damage in the tested sample.

In the case of adhesive joints, abrupt changes in normalized stiffness are generally caused by the separation (peeling off) of the joint elements. Such mechanisms were observed in the fatigue process of samples in which S&P Resin 220 and DP6310NS adhesives were applied. In both cases, detachment of the overlays (in the form of adhesive failure) occurred at their ends due to the existence of peel stresses (see Figure 4d). In this graph, the change in normalized stiffness $R$ for samples with the highest fatigue life is presented. Two samples with DP6310NS adhesive applied are shown in order to show the process of peeling off the overlays.

In the case of S&P Resin 220, such mechanisms were rapid and occurred shortly after starting the tests. This can be observed in Figure 5—in marked point (n/N_f = 0.1), the rapid reduction in the normalized stiffness was recorded due to the peeling off of certain end parts of the overlays. The detachment process of overlays bonded by polyurethane DP6310NS adhesive had a much lower intensity than those bonded by S&P Resin 220. Moreover, this phenomenon occurred after a much larger number of cycles (n/N_f = 0.3–0.5—see Figure 5). No detachment of the overlays was observed for HY 4080 GY cyanoacrylate/acrylic adhesive. In the case of this adhesive, a stable and constant degradation of the structure was achieved until its final fatigue failure. It is worth mentioning that for the HY 4080 GY adhesive, a high repetition of test results was observed. Slightly worse repetitiveness behavior was also observed for DP 6310 NS adhesive. The most scattered results were observed for S&P Resin 220, where the peeling of overlays was observed for different values of fatigue cycles.

3.4. Characterization of Failure Mechanisms for Particular Adhesives

Further investigation of the influence of the adhesive type and properties on the fatigue life of the steel/CFRP joint is studied by means of a detailed observation of fracture surfaces. Here, the comparison and measurements of fracture surfaces of steel cores with a focus on the sizes of the slow fatigue crack (with division into smooth and rough surface structure) and beach marks areas and sample narrowing Z (Equation (3)) were made:

$$Z\left(\%\right)={\displaystyle \frac{L_0-L_{fail}}{L_0}}100\%,$$

(3)

where $L_0$ and $L_{fail}$ are the initial length and length after failure, respectively.

3.4.1. S&P Resin 220

The samples in which S&P Resin 220 was used showed the shortest fatigue life. The exemplary photographs of the failed samples are presented in Figure 6. In all cases, S&P Resin 220 adhesive exhibited a brittle damage mechanism. The first damage forms in the adhesive layer (between the adhesive and steel core at the ends of the overlays) caused by peel stresses were initiated in the early phase of the fatigue test (Figure 5). It should be noted that such damage occurred for a smaller number of cycles than the fatigue life of core steel samples.

After the final failure, on the global scale, the failure form was the same; however, some differences were observed in the local damage forms. A strong adhesion to composite was obtained and there was no visible damage of the adhesive–composite interface. The main damage form was adhesive failure between the steel core and adhesive, and three different adhesive failure mechanisms between the steel and adhesive were noticed (Figure 7). The first is complete debonding, in which there was no trace of adhesive left on the steel core (Figure 6d and Figure 7a). In the second one, the very thin, rough and discontinuous adhesive layer (namely VTRDAL) remained on the steel (i.e., Zones A in Figure 6a and Figure 7b). The third and the least common damage form is related to cohesive failure, and in this case, a thick adhesive layer remained on the steel (Figure 6a—in zone B, Figure 6c, and Figure 7c).

Due to some differences in the local failure modes, the following detailed description for all tested samples is added. The description given below is related to the damage observed on the steel core:

• Sample no.1 (N_f = 56,282 cycles)—on two of four surfaces of the steel core on which adhesive failure occurred, the VTRDAL layers were observed (on the whole surfaces), including the areas around the rectangular notch and the crack edges. On the remaining two surfaces, adhesive was not observed (see Figure 7a).
• Sample no.2 (N_f = 94,423 cycles)—VTRDAL layers were partially observed on four surfaces (Figure 7b). On two surfaces, there was no adhesive layer around the notch and crack edges. On the remaining two surfaces, VTRDAL layers were present around the notch and crack edges. Small areas (in the form of islets) with cohesive failure were observed (Figure 7c).
• Sample no.3 (N_f = 82,169 cycles)—VTRDAL layers were partially observed on four surfaces, including zones around the notch and crack edges (Figure 8a).
• Sample no.4 (N_f = 65,576 cycles)—large areas with VTRDAL layers and without any adhesive layer. No adhesive layer was reported around the notch and cracks.

The application of cyclic loadings led to local chippings in the adhesive layer (Figure 8b). In places where the adhesive layer was degraded, the color of the adhesive surface changed from light gray to a dark gray color.

3.4.2. 3M Scotch-Weld DP6310DS

The exemplary failure forms of samples in which DP 6310 NS adhesive was used are presented in Figure 9. The main failure form of the interface was adhesive failure between the steel and adhesive. In the case of sample no.1 (Figure 9a,b), a noticeably stronger adhesion to steel was obtained than in the case of S&P Resin 220. In the case of the remaining two samples (i.e., Figure 9c,d), the areas where the adhesive interface between the steel and adhesive had not been completely damaged (Figure 10a) were much lower. Such areas were present in the neighborhood of the notches (Figure 9b–d and Figure 10a,b); however, there were no adhesive layers along crack faces.

DP 6310 NS adhesive revealed a strong adhesion to composite material, and only slight adhesive failure between adhesive and CFRP occurred (Figure 10c). Chipping, cracks and cohesive failure were also observed in the adhesive layer (Figure 10c). The damaged adhesive layer changed its color from dark green to light green and the adhesive structure became hard. At the steel/adhesive interface, four failure mechanisms were spotted—complete adhesive failure (Figure 11c), adhesive failure with an ultra-thin transparent layer of glue remaining on steel (Figure 11a) and cohesive failure (Figure 11b) with a thin and thick adhesive layer remaining on the steel core. Similar failure mechanisms were also observed on CFRP overlays (Figure 11d).

3.4.3. Loctite HY4080GY

Similar to the previous adhesives, the main damage form of the interface in the case of the application of the Loctite HY4080GY adhesive was adhesive failure at the steel–adhesive interface (Figure 12). However, in this case, the largest adhesion between the adhesive and steel was indicated. Moreover, what is particularly important is that it was observed that this adhesive showed the greatest adhesion in the vicinity of the notches and crack faces (Figure 13 and Figure 14). In contrast to previously discussed adhesives, serious damages in the adhesive–composite interface occurred. The complete and partial debonding of the adhesive layer from the composite surface were also observed, respectively, in Figure 12a and 12c.

In the surroundings of the failure zones of steel cores, complex failure mechanisms of the adhesive interface (with thin and thick adhesive layers remaining—Figure 13) are visible. The shearing and tearing effects seem to be dominant. Many short cracks in the adhesive layer were observed (Figure 13 and Figure 14). Such a damaged adhesive layer became harder and brittle. After the fatigue test, the adhesive retained its ductile behavior, but in the damaged areas, it was hardened. Small cohesive damages of the adhesive interface and composite overlays (a thin layer of fibers remained on the steel core) also occurred. The most typical failure was an adhesive failure; however, small zones with cohesive failure (in the vicinities of notches—Figure 13) were observed. It should be noted that the HY 4080 GY adhesive revealed the highest adhesion to both substrates (steel core and CFRP overlays) in the areas where the crack initiated and propagated (Figure 14).

3.5. FEM Results

Detailed numerical analyses were performed for the model proposed in Section 2.1 and static analysis was performed. Here the material data for the mild steel S355J2+N structural steel were taken from the tension test, while the data for CFRP overlays (T700/QY9511) are taken from the literature [46]. In order to compare the effectiveness of different adhesives, the set of simulations was performed for selected adhesives listed in Table 1 and Table 2. In this set, the thickness of the adhesive layer was set to t = 0.6 mm. The symmetric half of the investigated sample was subjected to static tension force Fmax = 47,500 N. The results of such studies are shown in Figure 15. There, the dependency between maximal stresses in the adhesive layer and the tensile modulus of the adhesive E_adh are illustrated. Here, the growth of the maximal stress both in the notch area and in the overlay end is observed. In the case of the notch area, the growth of the tensile stress ${\sigma }_x$ is the biggest, while in the case of the overlay end, the peeling stress ${\sigma }_z$ grows the most when E_adh increases. Keeping the level of stresses at an acceptable low level demands the application of relatively soft adhesives with a small Young’s modulus.

Following that observation, the detailed results of the numerical analysis are shown in Figure 16, Figure 17 and Figure 18. Here, the results are given for the DP6310 NS adhesive. Figure 16a shows the overall u_x displacement of the symmetric half of the investigated sample. The illustration of the predominant effects of stress concentration appearing in the notch area is shown in Figure 16b. In this area also, certain plastic deformations are reported. The distribution of them is shown in Figure 17a. In Figure 17b, the tension stresses in the CFRP overlay are presented, and their maximal values are observed in the vicinity of the notch area. Figure 18a,b show the distribution of the peeling stresses ${\sigma }_z$ in the adhesive and main shearing stresses ${\tau }_{xz}$, which are of the main importance in the adhesive static and fatigue destruction process. Their maximal values are close to the admissible ones given in Table 1.

4. Discussion

The performed experimental tests revealed the dominant influence of the adhesive type on fatigue life. The evaluation of the fracture mechanisms of the adhesive interface presented in the previous section confirms that adhesive is the weakest link and, at the same time, the decisive element for the durability of the entire structure. Based on the observation of the adhesive interface behavior and captured damage forms, the first conclusions can be drawn.

However, in order to analyze and assess in more detail the influence of adhesive properties on the fatigue of the entire structure, additional measurements of fatigue fractures were made. The exemplary images of the fatigue fracture zones are presented in Figure 19, Figure 20, Figure 21 and Figure 22. The images were selected in a way to present fracture zones for specimens with the smallest and highest fatigue lives for each adhesive. For each specimen, the photographs of both sides of the fracture zone are presented—on the left-hand side, the part with a larger fatigue area, and on the right-hand side, the part with a larger fast fracture zone.

The mentioned above measurements were limited to the assessment of fatigue damages occurring in the steel core. First of all, the areas with slow fatigue fracture zones were designated. Here, these areas were divided into two parts—smooth (designated as 1 in Figure 19, Figure 20, Figure 21 and Figure 22) and rough (designated as 2)—which differed in the smoothness of the fatigue failure zone. For better understanding, the specimens in Figure 19, Figure 20, Figure 21 and Figure 22 are arranged in order of increasing fatigue zones. Additionally, the areas with beach marks (designated as 3) and fast fracture growth (designated as 4) were approximately estimated.

The measurements were made for both sides of the hole of the steel core. Almost in all cases, cracks and fatigue damage were observed on both sides of the square hole. However, fatigue was always dominant on one side and on this side, a larger fatigue zone was observed (red bars in Figure 23 and Figure 24). Here, the average values measured for each group of samples are presented. The thin grey lines in these figures mean the standard deviations of the measured quantities.

The results performed for all specimens are shown in Figure 23 and Figure 24. The percentage contribution of smooth and rough slow fatigue fracture areas are shown in Figure 23a and Figure 23b, respectively. It can be seen that the obtained results for reinforced specimens have a clear trend regardless of whether the part with a higher or lower fatigue contribution is assessed. By grouping the samples from the smallest to the largest slow fatigue zone, the following order of adhesives is obtained: S&P Resin 220, DP 6310 NS and HY 4080 GY. Obviously, these fatigue areas for reinforced samples are larger than the fatigue areas of bare samples. Comparing reinforced and not-reinforced samples, it can be seen that in the case of the bare specimens, there were smaller differences in the sizes of the fatigue zones (both smooth and rough) on both sides of the notch.

The distance of the beach marks measured from the edge of the notch is shown in Figure 24a. The beach marks were not observed on the fracture zones of specimens in which HY 4080 GY was applied. This can be explained by the fact that the fatigue zones constituted most of the fracture zone (see Figure 23b, >90% and Figure 22a–c) or the entire part was subjected to a fast fracture (i.e., Figure 22d). In the remaining cases, the above-described trend was maintained (the range of beach marks is as follows, from the smallest to the largest: bare sample, S&P Resin 220 and DP 6310 NS).

The narrowing of the samples is shown in Figure 24b. Obviously, the largest narrowing was obtained for bare samples with similar values on both sides of the hole. The use of the reinforcement significantly reduces narrowing on one side (on which a larger fatigue zone occurred); however, on the second side, the observed narrowing was close (DP 6310 NS and HY 4080 GY) or larger (S&P Resin 220) than the values obtained for bare samples. This can be explained by the fact that the reinforcement relieved the steel core during damage growth (mainly on one side with a larger fatigue zone) and when the damage in the steel core reached a critical level, the adhesive joints are suddenly broken. This usually resulted in the fatigue damage on the second side (with a smaller fatigue zone) not having enough time to fully develop or not being initiated at all. This is also in agreement with the results presented in Figure 23 and Figure 24 for smaller fatigue zones in which the beach marks and the size of the slow fatigue fracture zones on bare samples are sometimes larger or comparable with those on the reinforced samples.

Different damage mechanisms were observed (Section 3.4) for the tested adhesive joints. The main failure form of degradation of the adhesive joints, which was observed in all cases, was adhesive failure between the steel and adhesive. The scale of the particular failure modes was specified for each sample. The obtained results are presented in Figure 25. The presented bars show the percentage participation of particular parameters on the measured damaged surfaces of the adhesive joint. The strongest adhesion of the adhesive to the steel core (in the range of 22–33%) was obtained for HY4080GY adhesive. In the case of S&P Resin 220, three adhesion failure forms were observed: 1—a thick adhesive layer remained on the steel core (0.5–4%), 2—a very thin adhesive layer remained on the steel core (24–78%), and 3—the complete lack of adhesion to steel (18–74%). The DP6310NS adhesive also revealed an unsatisfactory adhesion to the steel core (2.7–20%). The weakest adhesion to the composite was observed for HY4080GY adhesive (65–78%). The remaining adhesive (S&P Resin and DP6310NS) showed a high adhesion to the composite surface (99–100%). Slight composite damages were observed only in three cases and can be neglected in further analyses. A slight cohesion failure (below 3%) was observed in almost all cases, except for one specimen (DP 6310 NS—1) in which it achieved a value of 20.6%. In this case, it was caused by higher adhesion to the steel core. Finally, it can be observed that the fatigue life of samples in which S&P Resin 220 and DP 6310 NS were applied is correlated with adhesion to steel. On the other hand, in the case of the HY 4080 GY adhesive, the fatigue life seems to be correlated with adhesion to composite overlays.

In Section 3.5, it was shown that the stresses in an adhesive interface depend on its tensile modulus. This applies to normal and shear stresses at the ends of the overlays as well as in the surroundings of the notch in the steel core. All stresses increased (with a nonlinear parabolic trend) with increasing adhesive tensile modulus. So, the application of the stiff and strong adhesive may lead to failure due to the peel stresses, which rapidly increase at the end of the joint with an increase in the tensile modulus. This negative effect of peel stresses growth can be mitigated by using different adhesives (stiffer and stronger close to the notch and softer at the ends of the overlays) or by grading of the properties of the adhesive along the joint [6,47].

Based on the concluding remarks from the experiments that adhesions to steel and CFRP are most important for ensuring a high fatigue life, the obtained numerical results for different adhesives from Table 2 were compared with admissible tensile and shear stresses. The summary of this comparison is shown in Figure 26.

Here, it can be seen that adhesives with a low tensile modulus have also smaller admissible stress limits (both shear and tensile) than adhesives with a larger tensile modulus. However, the increase in tensile modulus results in increasing stresses in the adhesive interface, which, in many cases, exceed admissible limits. The admissible tensile stresses σ_z are exceeded in S&P Resin 220 (no. 11—in the surrounding of the hole and at the ends of overlays) and Sikadur 30 (no. 12—at the ends of overlays) adhesives. The admissible shear stresses at the adhesive/steel interface are exceeded for Araldite 2014-2 and S&P Resin 220 (in both cases, at the ends of overlays) and Sikadur 30 (at the ends of overlays and in the notch area). The admissible shear stresses at the adhesive/CFRP interface are exceeded for Araldite 2012, Araldite 2014-2 and S&P Resin 220 (at the ends of the overlays) and Sikadur 30 (at the ends of overlays and in the notch area). These observations explain the fatigue behavior of S&P Resin 220 (detachment of overlays and low fatigue life) revealed in the experimental tests and discussed in the previous section.

On the other hand, the performed FEM analyses and summary shown in Figure 26 do not explain the difference in fatigue life of samples with DP 6310 NS and HY 4080 GY.

It is most likely that the fatigue life, in these two cases, is additionally dependent on the adhesion forces of adhesive to the steel core. Adhesion to steel seems to be crucial because the first fatigue phenomena (plasticity, crack initiation and growth, etc.) occur in the steel core around the notch. Worse adhesion to steel was observed for DP 6310 NS. This led to detachments of the ends of overlays during the tests, which, consequently, also resulted in a change in stress redistribution in the adhesive interface and, finally, in accelerated fatigue damage growth. Another factor that should increase the fatigue life of samples with HY 4080 GY is that this adhesive seems to be the most resistant to the influence of peel stresses at the ends of the overlays. During tests with this glue, no symptoms of premature detachment of the overlays were observed. Moreover, HY 4080 GY revealed the highest adhesion to the steel core in the vicinity of the notch.

Finally, the selected properties of different adhesives are compared together in Figure 27 (2-C epoxy adhesives) and Figure 28 (2-C acrylic, polyurethane and methacrylate adhesives). Based on the performed study, the comparison concerned the following material properties: tensile modulus, shear strength on steel, shear strength on CFRP, tensile strength and elongation at failure. The comparison is presented in dimensionless form maintaining the scale of particular parameters. The minimal properties are close to the center of the wheel, while the largest ones are on the circumference of the circle. In the attached comparison, three adhesives are not shown—S&P Resin 220, Sikadur 30 and SikaFast 5221 NT. They are omitted to ensure the readability of the drawings because they have significantly different properties from other adhesives—a tensile modulus a few times larger (S&P Resin 220 and Sikadur 30) and an elongation at failure at least twice as large (SikaFast 5221 NT). Generally, epoxy adhesives (Figure 27) are characterized by a high tensile modulus, low elongation at failure and higher shear and tensile strengths. The remaining adhesives (Figure 28) reveal a smaller tensile modulus and strength but significantly higher elongation at failure.

Considering the reinforcement of metallic structures with CFRP overlays and under static loading conditions, stiff and strong adhesives are commonly used [30,44]. However, there are also critical comments regarding this approach [29]. It is worth mentioning that under cyclic loadings, the failure mechanisms are much more complex, and recommendations given for static loadings are no longer valid.

The performed study revealed that the value of the tensile modulus of adhesive has the strongest influence on the fatigue life. The increase in the adhesive modulus results in non-uniform and higher values of stresses—shear, peeling and normal stresses [19]. According to the observed results, the increase in peeling stresses is of the most importance and strongly affects fatigue life. It is also observed and confirmed in the literature [29] that the application of adhesives with a larger elongation at failure influences the distribution of shear stresses, resulting in their lower values and more uniform distribution over the whole area of bonding. It is obvious that the shear and tensile strength of the adhesives have crucial meaning for the fatigue strength. The best choice is to use adhesives with a small tensile modulus, high elongation at failure and high shear and tensile strengths. However, these demands are not possible to fulfill at the same time, because a reduction in the adhesive tensile modulus generally lowers the adhesive strength properties (Figure 26, Table 2). On the other hand, it can be seen that a reduction in the adhesive stiffness also reduces the stresses in the adhesive layer, and this reduction in stresses is significantly stronger (almost parabolic—see Figure 15) than the reduction in the mechanical properties of adhesives.

Following these results, it can be concluded that the primary criteria for adhesive selection (apart from the specific recommendations of adhesive manufacturers) are the tensile modulus and the elongation at failure. The admissible shear and tensile stresses in the adhesive should be treated as additional conditions of choice.

5. Conclusions

The performed experimental and numerical studies revealed the following conclusions:

• The adhesive joint is the weakest link in the studied reinforced structures subjected to cyclic loadings.
• 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.
• 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.
• 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.
• 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.
• Cyanoacrylate/Acrylic Hybrid Loctite HY4080GY 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.
• 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.