The object of the study is a structural silicone adhesive sealant. The aim of the work is to investigate the stress-strain state (SSS) of a bonded connection in hinged façade systems (HFS) using numerical analysis (finite element method, FEM) based on the results of experimental research. Method. During the study, experimental tests of a silicone adhesive sealant in combination with glass and aluminum were carried out. Based on the results of the experimental investigation, the favorable FE mesh refinement of the bonded connection into 3D FEs was selected for subsequent numerical calculations of HFS with adhesive-type cladding fixation. In addition, the suitable strength theory for evaluating the bonded connection according to the first group of limit states was identified based on the results of numerical modeling. Results. To determine displacements in HFS structures with bonded connections, the favorable FE mesh refinement in terms of the obtained results and the complexity of the computational model is an 8 × 8 FE mesh (FE size across the adhesive width not exceeding 2.75 mm; FE size through the adhesive thickness not exceeding 1 mm). With an 8 × 8 FE mesh refinement of the bonded connection, the stresses according to the first strength theory are significantly higher than the engineering stresses obtained from experimental studies. From the standpoint of stress evaluation in the bonded connection with an 8 × 8 FE mesh refinement, the fourth strength theory is appropriate.
1.Introduction
Bonded connections are widely used in various industrial sectors, including mechanical engineering, aeronautics, and aerospace engineering [1–3]. In these fields, they are characterized by high structural efficiency and a broad range of applications. In civil engineering, bonded connections are also increasingly employed, and research aimed at developing approaches to their application is actively ongoing [4]. It should be noted that bonded connections often function as load-bearing elements; therefore, accurate determination of adhesive material properties and the development of reliable calculation methods are required. A significant number of studies reported in the scientific literature are devoted to the evaluation of the mechanical properties of bonded connections and the standardization of methods for their determination [5–8]. In addition, numerous investigations have examined the behavior of bonded connections used in timber and metallic structural systems [9–11].
In addition to the strength criterion, adhesion plays an important role in the bonding process. Papers [12, 13] present the results of tests of various adhesive joints using different types of adhesives. The study [14] notes that an MS polymer-based adhesive sealant exhibits high adhesion to a wide range of construction materials. Furthermore, the quality of adhesion is significantly influenced by the use of surface pretreatment agents applied prior to bonding [15]. Study [16] demonstrates that, in order to form a durable adhesive joint, mechanical surface treatment in combination with chemical treatment is required.
Analytical evaluation of the stress-strain state (SSS) of bonded connections often encounters complexities due to the absence of exact analytical solutions [17, 18]. In this case, it is advisable to use numerical calculation methods. In references [19–21], numerical simulations of bonded connections were performed using the finite element method (FEM) implemented in software suites. In [22], the authors employed numerical modeling of adhesive joints and obtained results that are in good agreement with experimental data.
It should be emphasized that the widespread implementation of bonded connections is constrained by a scarcity of comprehensive data regarding factors influencing their strength and long-term durability. Publications [23–26] explore the impact of hygrothermal environmental conditions and other exogenous factors on the mechanical performance of bonded connections.
Issues related to the study of bonded connections are also actively addressed by researchers in other countries. In most of these works, the authors primarily focus on experimental investigations of bonded connections [27, 28]. In [29], experimental tests of bonded connections under shear loading showed that the type and thickness of the adhesive significantly affect the joint strength: increasing the plasticity and thickness of the adhesive layer increases the strength but reduces the stiffness of the joint. In [30], based on experimental tests, it was found that the overlap length, the thickness of the bonded material, and the overlap geometry (for example, wavy patterns or stepped configurations) significantly influence the fatigue performance of the joint, while some other parameters, such as fillets, have a negligible effect. It is also important to note that the results of experimental studies confirm the significant influence of cyclic loading on the durability of bonded connections [31].
In this study, the object of investigation is a structural silicone adhesive sealant. Applications of such bonded connections in hinged façade systems (HFS) have been previously investigated by domestic researchers. Reference [32] evaluates a calculation method for load-bearing bonded joints based on international regulatory frameworks [33]. In [34], a numerical study of silicone adhesive sealant, which is used in façade structures, was carried out. The implementation of bonded connections in HFS offers a superior alternative to traditional mechanical fastening, as it preserves the integrity of metallic components by eliminating the need for perforations or welding.
Based on the literature review, it is evident that a substantial knowledge base exists regarding the numerical modeling and calculation of bonded connections across multiple industrial fields. However, the specific behavior of bonded connections employing structural adhesive sealants within HFS has not been comprehensively investigated. Despite the similarity of the principles of calculating adhesive joints, the structural adhesive sealant used in façade structures has its own characteristics that must be taken into account in analytical and numerical calculation methods.
The present research aimed to investigate SSS of bonded connections in façade structures using FEM based on experimental results.
To achieve this aim, the following tasks were defined:
Conducting experimental tensile tests of a silicone adhesive sealant on specimens of two types. Determining a rational discretization scheme of the bonded connection into 3D FEs in a software package implementing FEM, based on the results of the experimental study (Type 1 specimen). Substantiating the selection of an appropriate strength theory for evaluating the bonded connection used as a fastening element of the cladding to the façade substructure according to the first group of limit states. Investigating the influence of considering geometric nonlinearity in determining the SSS of the bonded connection. Validating the developed numerical computational model by comparison with the results of experimental tests (Type 2 specimen).
The object of the study is a structural adhesive sealant. The subject of the research is the SSS of bonded connections in HFS.
2.Materials and Methods
Initially, the investigation of the bonded connection based on structural silicone was conducted through experimental testing. The specimens shown in Figs. 1 and 2 were subjected to testing. A glass element measuring 92 × 50 mm with a thickness of 8 mm was bonded to two aluminum tubes welded together (50 × 50 × 50 mm, wall thickness 2 mm) using a silicone adhesive sealant.
For Type 1 specimens (5 units), the adhesive joint was located at the center of the glass plate and the aluminum tube; the cross-sectional dimensions of the adhesive layer were 22 × 7 mm.
For Type 2 specimens (5 units), bonding was performed at the edge of the aluminum tube; the cross-sectional dimensions of the adhesive layer were 21 × 8 mm.
Due to the limited number of specimens, the obtained results should be considered preliminary and are mainly intended for comparison with the numerical analysis.
Figure 1. Specimen for experimental testing, Type 1.
Figure 2. Specimen for experimental testing, Type 2.
All test specimens were subjected to initial conditioning for at least 28 days after fabrication at a temperature of 23 ± 2 °C and a relative humidity of 50 ± 5 %.
The experimental study of the bonded connection was carried out using Zwick/Roell Z100 universal testing machine (Fig. 3) with maximum load capacity of 100 kN, manufactured by Zwick Roell AG (Ulm, Germany). During testing, the tensile loading rate of the specimens was maintained at 5 mm/min.
Figure 3. Zwick/Roell Z100 universal testing machine.
The subsequent stage of the study was devoted to the numerical modeling of the test specimens, including the determination of the appropriate FE mesh size for the silicone adhesive sealant and the selection of a suitable strength theory for evaluating the material according to the first group of limit states within the HFS.
To verify the static analysis of the bonded connection within a HFS, numerical models of the test specimens were developed using the SCAD Office software[1]. The bonded connection was modeled using volumetric FEs (FE Type 36). The connection between the glass, silicone adhesive sealant, and the aluminum tube in the computational model was implemented through shared FE nodes.
Examples of the numerical model in SCAD Office with an 8 × 8 FE mesh partition for the bonded connection for test specimens of Type 1 and Type 2 are demonstrated in Fig. 4.
Figure 4. Numerical models of the test specimens in SCAD Office: Type 1 specimen (left); Type 2 specimen (right).
The load application schemes using metal fixtures in SCAD Office are shown in Fig. 5.
Figure 5. Schemes of applying the experimental load in SCAD Office: Type 1 specimen (left); Type 2 specimen (right).
In the numerical models, support constraints in the X, Y, and Z directions were assigned at the locations where the test specimens were fixed in the universal testing machine (Fig. 6).
Figure 6. Assignment of support constraints in SCAD Office: Type 1 specimen (left); Type 2 specimen (right).
The bonding system consists of a two-component, high-modulus, neutral-cure structural silicone. The technical characteristics of the silicone bonded connection are as follows:
Design tensile strength:
Modulus of elasticity in tension or compression:
Shear modulus:
It is important to note that, according to regulatory documentation [33], the adhesive sealant used must exhibit a cohesive failure mode under both tensile and shear loading. In the case of adhesive failure, the use of this adhesive sealant as a fastening element for cladding in façade structures is not permitted.
The numerical models of the Type 1 specimen and the static analyses were performed with a gradual refinement of the FE mesh in the bonded connection region. After determining appropriate modeling conditions based on the experimental tests of the Type 1 specimen, the obtained parameters were validated using the numerical model of the Type 2 test specimen.
First, a series of static analyses of the Type 1 test specimen was performed with successive refinement of the FE mesh along the thickness and width of the bonded connection by a factor of two (Fig. 7). Six static analyses were carried out: 1 × 1 FE (22 × 7 mm); 2 × 2 FE (11 × 3.5 mm); 4 × 4 FE (5.5 × 1.75 mm); 8 × 8 FE (2.75 × 0.875 mm); 16 × 16 FE (1.375 × 0.438 mm); 32 × 32 FE (0.688 × 0.219 mm). The values in parentheses indicate the dimensions of a single solid FE along the width and thickness of the bonded connection, respectively.
1 × 1 FE
2 × 2 FE
4 × 4 FE
8 × 8 FE
16 × 16 FE
32 × 32 FE
Figure 7. FE mesh for the bonded connection.
For the purpose of improving the numerical models of the HFS involving bonded connection modeling, reduce the total number of FEs, and consequently decrease the computational time for static analyses, an additional series of numerical calculations was carried out. In these cases, the FE mesh of the bonded connection was refined only through the material thickness, while the number of elements along the width remained constant. An example of mesh refinement through the thickness with a 4-element subdivision along the width is shown in Fig. 8.
4 × 1 FE
4 × 2 FE
4 × 4 FE
4 × 8 FE
Figure 8. FE mesh refinement through the thickness of the bonded connection.
Similarly, numerical models with various FE subdivisions of the bonded connection were developed and analyzed. Ultimately, static calculations were performed for the following partitions:
2 FE: 2 × 1 FE (11 × 7 mm); 2 × 2 FE (11 × 3.5 mm); 2 × 4 FE (11 × 1.75 mm); 2 × 8 FE (11 × 0.875 mm); 2 × 16 FE (11 × 0.438 mm); 2 × 32 FE (11 × 0.219 mm); 4 FE: 4 × 1 FE (5.5 × 7 mm); 4 × 2 FE (5.5 × 3.5 mm); 4 × 4 FE (5.5 × 1.75 mm); 4 × 8 FE (5.5 × 0.875 mm); 4 × 16 FE (5.5 × 0.438 mm); 4 × 32 FE (5.5 × 0.219 mm); 8 FE: 8 × 1 FE (2.75 × 7 mm); 8 × 2 FE (2.75 × 3.5 mm); 8 × 4 FE (2.75 × 1.75 mm); 8 × 8 FE (2.75 × 0.875 mm); 8 × 16 FE (2.75 × 0.438 mm); 8 × 32 FE (2.75 × 0.219 mm).
The values in parentheses indicate the dimensions of a single solid FE along the width and thickness of the bonded connection, respectively.
In order to study the influence of geometric nonlinearity on the SSS of the bonded connection, static nonlinear analyses were performed in SCAD Office with the following FE discretizations of the bonded connection:
4 × 8 FE (5.5 × 0.875 mm); 8 × 8 FE (2.75 × 0.875 mm); 32 × 32 FE (0.688 × 0.219 mm).
The values in parentheses indicate the dimensions of a single solid FE along the width and thickness of the bonded connection, respectively.
The bonded connection incorporating geometric nonlinearity was modeled using volumetric FEs (FE Type 336). The nonlinear analysis was performed using a simple incremental method until the load reached 300 N with a load step of 10 N (a total of 30 increments).
3.Results and Discussion
Experimental Results
During the experimental study, the cross-sectional area of the bonded connection, the breaking load, and the test duration were determined (Tables 1 and 2).
Table 1. Test results (Type 1 specimen).
No.
S0 (mm2)
Fmax (MPa)
t (sec)
1
1124.98
0.970
309.62
2
1088.82
1.170
285.47
3
1080.14
0.764
255.39
4
1278.24
0.911
327.21
5
1145.24
1.100
223.53
Table 2. Test results (Type 2 specimen).
No.
S0 (mm2)
Fmax (MPa)
t (sec)
1
1008.10
1.169
152.24
2
1150.82
1.147
238.7
3
1117.70
1.074
326.49
4
1069.88
1.168
311.79
5
1029.62
1.158
305.8
As a result of the conducted tests, diagrams showing the dependence of displacements and conditional stresses on the applied load were also obtained for the Type 1 test specimen (Figs. 9 and 10).
Figure 9. Dependence of displacements on applied load (Type 1 specimen).
Figure 10. Dependence of engineering stresses on applied load (Type 1 specimen).
Similar dependencies were obtained for the Type 2 test specimen (Figs. 11 and 12).
Figure 11. Dependence of displacements on applied load (Type 2 specimen).
Figure 12. Dependence of engineering stresses on applied load (Type 2 specimen).
Engineering stresses in the bonded connection, presented in the diagrams, were determined according to the following formula:
(1)
where is the tensile load acting on the test specimen; is the cross-sectional area of the bonded connection, oriented orthogonally to the load application vector.
According to ETAG 002, the stresses occurring in the center of the longest bonded joint can be determined by the following formula:
(2)
where is the peak wind pressure acting on the cladding element; is the length of the short side of the cladding element; is the width of the bonded joint.
Based on (2), the stresses in the longest bonded joint can be determined using the following formula:
(3)
where is the tributary width of wind load.
The total tensile force acting on the bonded connection can be determined by the following formula:
(4)
where is the length of the bonded joint.
Thus, by expressing the peak wind pressure from (4) and substituting it into (3), the following expression is obtained:
(5)
Therefore, the determination of engineering stresses in the bonded connection using (1) is consistent with the stress determination method according to ETAG 002 using (2).
The deformations of the bonded connection under the action of the tensile load in the testing machine are shown in Fig. 13.
Figure 13. Deformations of the bonded connection (Type 1 specimen).
Tensile testing of the specimens was conducted until failure of the bonded connection. Cohesive failure occurred in all tests. The failed specimen is shown in Fig. 14.
Figure 14. Failed specimen (Type 1 specimen).
Results of Numerical Investigation with FE Mesh Refinement through the Thickness and Width of the Bonded Connection
An analysis of the relationships presented in Figs. 10 and 12 shows that the conditional stresses arising in the bonded connection reach the design resistance value at a test load level of up to 200 N.
Therefore, the assessment of the displacements of the test specimen and the stresses arising in the bonded connection, based on the calculation results obtained using the SCAD Office software package, was performed within the load range from 0 to 200 N.
During the numerical analysis, the displacements of the test specimen and the stresses according to the 1st, 3rd, and 4th strength theories were evaluated. The results of the numerical calculations performed in SCAD Office with a sequential refinement of the FE mesh along the thickness and width of the bonded connection are presented in Table 3. Since the analysis in SCAD Office was carried out within a linear formulation, a single calculation point is sufficient to construct the dependency diagram.
Table 3. Results of calculations in SCAD Office.
FE mesh
Load (N)
Displacements (mm)
Stresses 1st strength theory (MPa)
Stresses 3rd strength theory (MPa)
Stresses 4th strength theory (MPa)
1 ´ 1
0
0
0
0
0
200
0.13
0.175
0.007
0.007
2 ´ 2
0
0
0
0
0
200
0.23
0.197
0.042
0.036
4 ´ 4
0
0
0
0
0
200
0.34
0.237
0.12
0.104
8 ´ 8
0
0
0
0
0
200
0.39
0.258
0.198
0.172
16 ´ 16
0
0
0
0
0
200
0.41
0.307
0.261
0.226
32 ´ 32
0
0
0
0
0
200
0.42
0.407
0.322
0.279
A comparison of the results of numerical modeling and experimental studies is presented in the diagrams shown in Figs. 15–18. The results of the experimental study were averaged and presented as a single generalized graph.
Figure 15. Dependence of displacements on applied load.
Figure 16. Dependence of maximum principal stresses on the applied load.
Figure 17. Dependence of equivalent stresses (3rd strength theory) on the applied load.
Figure 18. Dependence of equivalent stresses (4th strength theory) on the applied load.
According to the results presented in Table 3, the displacement values in the computational model with mesh divisions of 16 × 16 and 32 × 32 FEs differ by:
Thus, further refinement of the FE mesh was not performed, since the increase in displacements in the computational models did not exceed 5 %. At the same time, further reduction in the size of FEs could increase the probability of numerical errors in stress determination associated with the application of the FEM.
The following conclusions can be drawn from the obtained diagrams:
For determining displacements within the considered load range, an appropriate mesh, considering both the obtained results and the computational model complexity, is the 8 × 8 FE discretization (the difference in displacements does not exceed 7 %). With an 8 × 8 FE discretization of the bonded connection, the stresses determined according to the 1st strength theory are significantly higher (by 47 %) than the nominal stresses obtained from the experimental study. The stress results obtained according to the 3rd and 4th strength theories with an 8 × 8 FE discretization show the closest agreement with the nominal stresses obtained experimentally. The difference is 13 % according to the 3rd strength theory and 2 % according to the 4th strength theory. From the standpoint of evaluating the stress state of the bonded connection with an 8 × 8 FE discretization, the 4th strength theory is appropriate. Another study [34] also notes that the 4th strength theory allows the most accurate assessment of sealant adhesive failure.
Numerical Study Results for FE Mesh Refinement Across the Thickness of the Bonded Connection
The results of numerical calculations in SCAD Office software with sequential FE mesh refinement across the thickness of the bonded connection and their comparison with the experimental study results are presented in the diagrams. The results of the experimental study were averaged and presented as a single graph.
Partitioning of the bonded connection into 2 FEs across the width and FE mesh refinement across the thickness (Figs. 19–22).
Figure 19. Dependence of displacements on applied load.
Figure 20. Dependence of maximum principal stresses on the applied load.
Figure 21. Dependence of equivalent stresses (3rd strength theory) on the applied load.
Figure 22. Dependence of equivalent stresses (4th strength theory) on the applied load.
Partitioning of the bonded connection into 4 FEs across the width and FE mesh refinement across the thickness (Figs. 23–26).
Figure 23. Dependence of displacements on applied load.
Figure 24. Dependence of maximum principal stresses on the applied load.
Figure 25. Dependence of equivalent stresses (3rd strength theory) on the applied load.
Figure 26. Dependence of equivalent stresses (4th strength theory) on the applied load.
Partitioning of the bonded connection into 8 FEs across the width and FE mesh refinement across the thickness (Figs. 27–30).
Figure 27. Dependence of displacements on applied load.
Figure 28. Dependence of maximum principal stresses on the applied load.
Figure 29. Dependence of equivalent stresses (3rd strength theory) on the applied load.
Figure 30. Dependence of equivalent stresses (4th strength theory) on the applied load.
The presented diagrams clearly demonstrate the results, on the basis of which the following conclusions can be formulated:
To refine the static analysis of HFS with bonded connections, FE mesh refinement across the thickness of the bonded connection is of primary importance. To simplify the numerical model of the HFS when modeling the bonded connection and determining displacements, FE meshes of 2 × 8 and 4 × 8 may be used. The displacement values obtained using these meshes differ from the experimental data by no more than 5 %. However, the application of the 4th strength theory for evaluating stresses in the bonded connection with these mesh configurations is inappropriate, since the calculated stresses are 24–83 % lower than the values obtained from the experimental study. Results of Numerical Investigation Considering Geometric Nonlinearity
The results of nonlinear calculations in the SCAD Office software suite, considering the geometric nonlinearity of the bonded connection’s volumetric FEs, are summarized in the diagrams (Figs. 31 and 32).
Figure 31. Dependence of displacements on applied load.
Figure 32. Dependence of equivalent stresses (4th strength theory) on the applied load.
The following conclusions can be drawn from the obtained diagrams:
Taking geometric nonlinearity into account, the displacement results obtained from experimental studies and numerical simulations show good agreement provided that the bonded connection is discretized with a mesh no finer than 8 × 8 FEs and the applied load does not exceed 50 N. With further mesh refinement (up to 32 × 32 FEs), the displacement values remain consistent with the experimental data up to a load of 105 N. At higher load levels, the numerical model with the bonded connection and geometric nonlinearity demonstrates a significant increase in stiffness, which does not correspond to the experimental results. Stress analysis according to the 4th strength theory for a bonded connection modeled with geometrically nonlinear FEs leads to significant discrepancies (from 24 to 60 %) compared with experimentally obtained stress values. A mesh of 8 × 8 FEs provides a conservative stress assessment with a safety margin of approximately 33 %. These factors indicate the need to refine the numerical model by accounting for the physical nonlinearity of the material. In modeling the HFS with geometric nonlinearity taken into account, the bonded connection should be represented using geometrically linear 3D FEs. Otherwise, the stiffness of the HFS numerical model will be significantly overestimated. Validation of the Obtained Modeling Conditions for the Silicone Adhesive Sealant
In order to verify the validity of the previously established modeling conditions for the silicone adhesive sealant, a validation study was performed based on the results of tests of Type 2 specimen, which is characterized by a different bonding configuration and different cross-sectional dimensions of the bonded connection.
The validation was carried out through the analysis of load–displacement diagrams obtained during the experimental study (Figs. 11 and 12).
The silicone adhesive sealant in the numerical model of Type 2 specimen was simulated using 3D FEs (FE Type 36) with the bonded connection discretized by an 8 × 8 FE mesh. The FE size along the width of the bonded connection was 2.625 mm, while the element size through the thickness was 1 mm.
A comparison of the displacement values obtained from the numerical simulation and the experimental study is presented in Figs. 33 and 34.
Figure 33. Dependence of displacements on applied load (Type 2 specimen).
Figure 34. Dependence of equivalent stresses (4th strength theory) on the applied load (Type 2 specimen).
Based on the interpretation of the obtained diagrams, the following conclusions can be drawn:
Discretization of the adhesive joint using an 8 × 8 mesh of linear 3D FEs in numerical modeling provides displacement values that differ from the results of experimental studies by no more than 7 %. In the evaluation of the stress state of the silicone adhesive sealant according to the 4th strength theory using an 8 × 8 FE discretization, it was found that the obtained stress values differ from the results of experimental tests by approximately 4 %.
4.Conclusions
The main conclusions and results of the conducted study are as follows:
The experimental study was limited to two types of specimens and a small number of tests; therefore, the obtained results are preliminary. Further experimental studies with a larger number of specimens are required to obtain statistically reliable characteristics of the bonded connection. It is proposed to determine displacements in HFS with bonded connections using discretization of the adhesive layer into an 8 × 8 FE mesh (the FE size along the adhesive width should not exceed 2.75 mm; through the adhesive thickness, not more than 1 mm). The displacement values obtained using this discretization differ from the experimental results by no more than 7 %. It was established that when the bonded connection is discretized using an 8 × 8 FE mesh, the stresses determined according to the 1st strength theory are significantly higher (up to 47 %) than the nominal stresses obtained from experimental studies. This result indicates that stress analysis based on principal stresses leads to an excessive safety margin for the bonded connection. It is proposed that, when using the 8 × 8 FE discretization of the bonded connection, stresses should be evaluated according to the 4th strength theory. In this case, the deviation from the experimental results ranges from 2 to 4 %. It has been shown that, to improve the accuracy of static analyses of HFS with bonded connections, a significant factor is the refinement of the FE mesh of the adhesive layer through its thickness. To simplify the computational model of HFS with bonded connections and to determine displacements, discretization schemes of 2 × 8 FEs (FE size through the adhesive thickness not exceeding 1 mm and along the width not exceeding 11 mm) and 4 × 8 FEs (FE size through the adhesive thickness not exceeding 1 mm and along the width not exceeding 5.5 mm) may be used. These discretization schemes provide good agreement with experimentally obtained displacement values (up to 5 %). However, this modeling approach is not appropriate for evaluating the bonded connection according to the first group of limit states, since the calculated stresses differ from the experimental values by 24–83 %. Therefore, these discretization schemes are recommended only for preliminary static analyses of HFS with bonded connections. In analyses that take geometric nonlinearity into account, the results of experimental studies and numerical modeling are consistent only at the initial stage of loading (up to 105 N). In this case, the stress assessment in the bonded connection provides a safety margin of up to 33 %. As the load increases, the computational model with geometric nonlinearity demonstrates a significant increase in stiffness, which does not correspond to the experimental results. Thus, it has been established that in modeling HFS with consideration of geometric nonlinearity, the bonded connection should be represented by geometrically linear 3D FEs. Otherwise, the stiffness of the computational model of the HFS will be significantly overestimated.