Mechanical behaviour of Transparent Structural Silicone Adhesive (TSSA) steeltoglass laminated connections under monotonic and cyclic loading
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Abstract
Steeltoglass laminated connections, which have recently been developed, limit stress intensifications on the glass and combine strength and transparency. Transparent Structural Silicone Adhesive (TSSA) connections have been used in several projects worldwide; however, the hyperelastic and viscoelastic nature of the material has to date not been fully investigated. In this work, the first objective is to investigate the mechanical response of TSSA connections under static and cyclic loading by means of experimental tests. Firstly, the shear behaviour of TSSA circular connections is characterized by means of monotonic and cyclic loading tests. The adhesive exhibits significant stresssoftening under repeated cycles that becomes more severe as the maximum load increases. Secondly, TSSA circular connections are subjected to monotonic and cyclic tensile loading of increasing maximum load. The way whitening propagates on the adhesive surface shows some consistency comparing the cases of static and cyclic loading. The second objective is to analytically describe the deformation behaviour of the adhesive based on hyperelastic prediction models. Uniaxial and biaxial tension tests are combined with the simple shear tests, for the material characterization of TSSA. The hyperelastic material parameters are calibrated by a simultaneous multiexperimentdatafit based on the nonlinear least squares optimization method. The softening behaviour observed in shear tests is modeled based on a simplified pseudoelastic damage model proposed by Ogden–Roxburgh. A first attempt is also made to model the actual softening response of the adhesive. A less conservative approach proposed by Guo, also based on the theory of pseudoelasticity, proved to give a good approximation of the actual cyclic response of the adhesive.
Keywords
Glass TSSA Silicone Mullins effect1 Introduction
1.1 Transparent Structural Silicone Adhesive
Transparent Structural Silicone Adhesive is a crystal clear silicone adhesive film produced by Dow Corning that exhibits thermal stability and excellent weatherability (Sitte et al. 2011). It was developed for frameless glazed facade applications with steel to glass laminated adhesive connections. It is an elastomeric onecomponent addition cured silicone with no byproducts (and no odor), characterized by nanosilica and crosslinked polymers (Santarsiero et al. 2016a). TSSA laminated connections have been used in several projects, such as the Dow Corning’s new European Distribution Centre in Belgium. In this project, TSSA frameless spider connections allowed the use of insulated glazed units, easier fabrication on site and avoided drilling the glass.
Overend et al. (2013) tested TSSA single lap joints and Tpeel specimens. The results showed that TSSA exhibits sufficient strength in combination with a flexible behavior, which is unique among other transparent heatcuring foils, such as SentryGlas. In the work of Sitte et al. (2011), the tensile and shear monotonic behavior of TSSA connections was investigated at room temperature. In addition, the behaviour of TSSA bulk material was also investigated at a constant displacement rate. The results showed that TSSA exhibits a hyperelastic response. Cyclic loading tests were also performed, and results showed the appearance of the stress softening phenomenon, also referred to as Mullins effect.
In the work performed by Santarsiero et al. (2016b), TSSA dumbbell shaped specimens were subjected to uniaxial tensile tests. The tests were performed at different temperatures (\(\,20, 23\) and \(80\,{^{\circ }}\hbox {C}\)) and displacement rates (1, 10 or 100 mm/min). A nonlinear stress–strain response was also observed, confirming the hyperelastic nature of TSSA. Temperature variations did not significantly influence the stiffness of the adhesive; however, the stress and strain at the point of failure showed a temperature dependency. Santarsiero et al. (2016a) also performed shear and tensile tests on TSSA laminated circular connections. The specimens consisted of annealed glass plates with a laminated stainless steel circular button with diameter 50 mm. The shear behaviour of those connections proved to be mainly linear until failure, a fact which was also observed in the work of Hagl et al. (2012) and Sitte et al. (2011). On the other hand, the mechanical response of laminated circular connections under tensile load appeared to be bilinear, showing a very stiff response followed by a hardening phase. The influence of temperature on the shear and tensile behaviour of the connection proved to be negligible.
Tensile tests of TSSA dumbbells and TSSA metal to glass connections (Santarsiero et al. 2016b; Sitte et al. 2011) have showed that the adhesive does not remain transparent throughout testing. Its colour changes from completely transparent to white above a certain stress level. According to the manufacturing company, Dow Corning\({\textregistered }\), the whitening phenomenon is expected when the local stress exceeds 2 MPa. In the work of Santarsiero et al. (2016a) and Sitte et al. (2011), the whitening of TSSA is clearly visible at engineering stresses close to 5 MPa.
1.2 The Mullins effect
Elastomer or rubberlike materials, such as TSSA, undergo a stress softening phenomenon under cyclic loading. More specifically, they exhibit a hysteretic behaviour, which is characterized by a difference between the loading and unloading mechanical response. This softening effect, also referred to as the Mullins effect, was first extensively studied by Mullins (1969) in the 1970’s. More specifically, the Mullins effect describes the dependency of the stress–strain curve of rubbers on the maximum load previously encountered. When the load is less than the previous maximum load, the loading response of rubbers follows the path of the undamaged ‘virgin’ material, whereas the unloading response is characterized by a softening behaviour. Whenever the load increases above its prior maximum value, the stress–strain curve changes, resulting in more severe softening behaviour.
Several physical interpretations have been proposed to understand the stresssoftening phenomenon of rubbers. However, there is still no universal consensus on the origin of this phenomenon (Diani et al. 2009). Blanchard and Parkinson (1952) expressed the theory that the stresssoftening effect is the result of bond ruptures taking place during stretching. According to their theory, the weaker bonds (or physical bonds) are ruptured first, followed by the stronger (or chemical) bonds. Houwink (1956) used instead the theory of molecules slipping over the surface of fillers, as a fact which causes new bonds to be created. These new bonds are of the same physical nature, but they are located at different places along the rubber molecules (Diani et al. 2009). According to this theory, the phenomenon could be reversible with exposing the rubber to elevated temperatures. Other theories have been developed by Kraus et al. (1966) who attribute the stresssoftening effect to the rupture of carbonblack structure, which is used as reinforcing filler in many rubber products.
1.3 Objectives
The monotonic response of TSSA dumbbell specimens and TSSA laminated circular connections has been already investigated by Hagl et al. (2012), Santarsiero et al. (2016b) and Sitte et al. (2011). However, very few experimental data exist on the cyclic behaviour of TSSA, and the appearance of the Mullins effect.
In this study, TSSA laminated circular connections with diameter 50 mm are subjected to a series of monotonic and cyclicshear and tensile tests. The first objective is to study the mechanical response of these connections under loading cycles and to observe if they exhibit the stresssoftening phenomenon. Secondly, the development of the whitening phenomenon will be compared under monotonic and cyclic loading. Thirdly, the propagation of whitening both for the cases of static and cyclic loading and the recovery of the phenomenon when removing the load is studied.
Even though significant research has been performed on the mechanical response and the stress state of circular TSSA connections, as well as a generalized failure criterion has been developed by Santarsiero et al. (2018), limited information can be found in literature on the nonlinear TSSA constitutive law. This makes it difficult to produce a finite element model that sufficiently describes the behaviour of TSSA laminated connections under certain specific stress states. The behaviour of elastomeric materials, such as TSSA, can be described by a broad range of hyperelastic nonlinear constitutive laws, most of which can be implemented in finite element software to describe the behaviour of elastomers. The accuracy of the predicted mechanical response largely depends on the chosen model. Therefore, the final objective of this study is the calibration of several material models based on experimental data and the assessment of the suitability of each model to describe the stress–strain response of the adhesive.
2 Method
2.1 Materials and specimens
2.2 Shear test setup
The relative displacement between the glass and the connector is measured by two Linear Variable Differential Transformers (LVDTs) with a stroke of \(\pm \,5\,\hbox { mm}\) which are placed on the right and left side of the connector. The LVDTs stand on two small aluminium Lprofiles, which are bonded on the glass surface. In this way, it is possible to measure the relative displacement of glass and steel and thus the displacement of the adhesive. The behaviour of TSSA in shear is recorded on video during the tests, as the setup allows visual inspection of the adhesive through the glass pate.
A series of static and cyclic tests are performed at average room temperature of \(27\,\pm \,0.04\,{^{\circ }}\hbox {C}\). The monotonic tests are performed in displacement control at a displacement rate of 1 mm/min. The cyclic tests are conducted in force control and loading cycles are performed from 0 to +P or from −P to +P (where P refers to the maximum load level of the cycle) at 0.1 or 1 Hz. The loading pattern is based on the guideline ETAG 002 (EOTA Recommendation 2001), which specifies a trapezoidalshaped function with time for mechanical fatigue tests of structural sealants. The guideline describes a linear increase of load with time, followed by a stable phase where the maximum (or minimum load) remains constant to counteract creep effects. When unloaded, a steady state of zero (or nearly zero) loading follows. In this way, the mechanical response of the adhesive is isolated, as much as possible, from viscoelastic effects related to creep or relaxation, in order to derive the timeindependent response of TSSA. Cycles are performed at different load levels that begin from a loading loop of 0 to 1 or \(1\) to 1 kN, which is repeated 50 times. Subsequently the maximum (and minimum) load increases in absolute terms with a step of 1 kN every 50 cycles. Loading cycles are performed up to 8 kN. Performing cycles up to this load level would avoid failure of the specimen during cyclic loading, since previously recorded failure loads range between 9.3 and 11.9 kN (Santarsiero et al. 2016a). Data are acquired with a frequency of 10 Hz.
Figure 4 illustrates the load versus time relation. The left graph describes the tests that involve reverse shearing, whereas the right graph describes shearing in only one direction. The duration of the steady state of the load is indicated either with t1, when the load is maximum, or t2, when the load is nearly zero. The values of t1 and t2 (t1 \(=\) t2) are 2 or 0.2 s corresponding to frequencies 0.1 and 1 Hz.
2.3 Tensile test setup
Tests performed in this research
Test types  Stress state  Displ. rate/frequency  Number of tests 

Static  Shear  1 mm/min  3 
Tensile  1 mm/min  3  
Cyclic  Shear  0.1 Hz—one direction shear  3 
0.1 Hz—two direction shear  3  
1 Hz—two direction shear  3  
Tensile  0.1 Hz  4  
1 Hz  3 
A series of static and cyclic tests are performed at average room temperature of \(23.7\,\pm \,2.3\,{^{\circ }}\hbox {C}\). It must be noted that room temperature differences are not expected to influence the results, since TSSA exhibits stability against temperature variations (Santarsiero et al. 2016a). The static tests are performed in displacement control at a displacement rate of 1 mm/min. The cyclic tests are conducted in force control and the specimens are subjected to loading cycles under two different frequencies of 0.1 and 1 Hz. The loading pattern follows again the trapezoidal form described in the guideline ETAG 002. Loading cycles are performed at different load levels. The cycles begin from a loading loop of 0 to 1 kN that is repeated 50 times. Subsequently, the maximum load increases with a step of 1 kN every 50 cycles. The specimens are loaded up to a maximum load of 8 kN. Data are acquired with a frequency of 10 Hz.
2.4 Tests summary
The summary of the tests performed is given in Table 1.
3 Experimental results
3.1 Shear test results
3.2 Tensile test results
4 Analytical modeling
When numerically analyzing adhesive pointfixings using a finite element software, the accuracy of the results largely depends on the predefined material model. The glass and steel elements can be simulated with linear elastic properties; however, adhesives, such as TSSA, require specific mathematical expressions to describe their behaviour. The suitability of the model is assessed by curve fitting various mathematical expressions to experimental data that is generated in the current paper and experimental data derived from literature.
4.1 Theoretical background
4.2 Method
Derivation of stresses according to the uniaxial, shear and equibiaxial deformation tests

4.3 Modeling the stresssoftening phenomenon
Several continuum mechanics and pseudoelastic models exist that describe the stresssoftening phenomenon observed in elastomers. In practice, few of them are used and are commercially available in finite element analysis software. Such modes were proposed by Simo (1987), Govindjee and Simo (1991), Ogden and Roxburgh (1999), Chagnon et al. (2004), Qi and Boyce (2004) and many others. It must be noted that these models can describe only a small fraction of the structural properties of elastomers, since the mechanical response of these materials changes constantly with the number of cycles. The models based on continuum mechanics theory are considered complex and computationally demanding. On the other hand, most finite element software make use of pseudoelastic material models (see “Appendix B”) that make use of a damage parameter to describe the loading path with a common strain energy function and the unloading and reloading paths with a different strain energy function that is based on the undamaged situation.
5 Discussion
Material constants and coefficient of determination of the Neo–Hooke, Mooney–Rivlin and Gent–Thomas models
Material models  Coefficients  

Neo–Hooke  \(\hbox {C}_{10}\)  1.315 
\(\hbox {R}_{\mathrm{UT}}^{2}\)  0.7880  
\(\hbox {R}_{\mathrm{S}}^{2}\)  0.9929  
\(\hbox {R}_{\mathrm{BT}}^{2}\)  0.8563  
Mooney–Rivlin (2parameter)  \(\hbox {C}_{10}\)  1.159 
\(\hbox {C}_{01}\)  0.1554  
\(\hbox {R}_{\mathrm{UT}}^{2}\)  0.9076  
\(\hbox {R}_{\mathrm{S}}^{2}\)  0.9929  
\(\hbox {R}_{\mathrm{BT}}^{2}\)  0.8698  
Gent–Thomas  \(\hbox {C}_{10}\)  1.158 
\(\hbox {C}_{01}\)  0.6500  
\(\hbox {R}_{\mathrm{UT}}^{2}\)  0.9671  
\(\hbox {R}_{\mathrm{S}}^{2}\)  0.9960  
\(\hbox {R}_{\mathrm{BT}}^{2}\)  0.8076 
In Fig. 18, the calculated dissipated energy in MPa (or \(10^{6}\,\hbox {J/m}^{3})\) is plotted against the number of cycles. It is typical in rubbers exhibiting the stress softening phenomenon, that during the first cycle a large amount of energy is dissipated. This is in fact observed in the work of Sitte et al. (2011), where TSSA was subjected to uniaxial, shear and equibiaxial cyclic tests. After the first cycles the dissipated energy of rubbers either gradually decreases, in case of displacement controlled tests, due to relaxation, or increases, in case of force controlled tests, due to creep. The latter is in fact observed in the shear test results performed for purpose of this study, since the tests are carried out in force control.
Damage parameters and coefficients of determination based on the Ogden–Roxburgh model
Material models  Coefficients  Maximum applied load to the connection  

1 kN  2 kN  3 kN  
Ogden–Roxburgh and Mooney–Rivlin  m  0.591  3.651  0.985 
r  0.256  0.110  0.586  
b  0.201  0.144  0.180  
\(\hbox {R}^{2}\)  0.9640  0.9767  0.9922  
Ogden–Roxburgh and Gent–Thomas  m  0.065  0.214  0.230 
r  1.467  1.419  1.320  
b  0.016  \(9.55\times 10^{9}\)  0.500  
\(\hbox {R}^{2}\)  0.9879  0.9943  0.9956 
Damage parameters and coefficients of determination based on the Guo model
Material model  Coefficients  Maximum applied load to the connection  

1 kN  2 kN  3 kN  4 kN  5 kN  
Guo and Mooney–Rivlin  m  34.392  21.361  2.641  0.617  0.442 
r  0.121  0.125  0.00025  1.537  1.503  
\(\hbox {m}_{1}\)  0.079  0.816  1.662  0.365  0.839  
\(\hbox {r}_{1}\)  0.063  0.017  0.640  0.491  0.628  
\(\hbox {R}_{\mathrm{loading}}^{2}\)  0.9688  0.9816  0.9924  0.9962  0.9930  
\(\hbox {R}_{\mathrm{unloading}}^{2}\)  0.7914  0.8896  0.9531  0.9742  0.9675 
6 Conclusion
This research focused on investigating the static and cyclic mechanical response of TSSA laminated circular connections under shear and tensile loading. The shear cyclic response showed significant stress softening that depends on the maximum load previously encountered and the applied frequency. This softening behaviour deviates from the static response, which appears to be mainly linear, and thus a nonlinear constitutive law is needed to simulate the cyclic response of TSSA. The mechanical response of the connections subjected to reverse shearing appears to be the same in both directions, meaning that there is no need to account for any divergence of the response between “positive” and “negative” shear, when it comes to the simulation of the deformation behaviour. Tensile cyclic loading tests showed that the stresssoftening phenomenon starts to develop at very high stress levels above the working limit of the connection. Furthermore, the propagation of the whitening phenomenon appeared to be similar under static and cyclic loading. Whitening completely disappears when the load is removed, a fact which must be carefully considered in case the phenomenon is utilized as a warning for overloading. In civil engineering practice, stress peaks usually appear instantaneously, a fact which means that whitening is expected to occur instantly. Nevertheless, the propagation of the whitening effect shows some consistency, a fact which is considered advantageous as it may be used as an indicator of the quality of bonding in nondestructive quality assurance testing. Finally, the shear tests were combined with uniaxial and biaxial test data to calibrate various hyperelastic models for the simulation of the mechanical response of TSSA. The softening behaviour observed in shear tests was modeled based on the simplified approach proposed by Ogden and Roxburgh. A less conservative approach was suggested based on the model of Guo, which provides a good approximation of the actual cyclic response of the adhesive. This model may be implemented in FE analysis through a userdefined subroutine and be used to predict the changes in stiffness observed during the tests.
Notes
Acknowledgements
The authors would like to thank Glas Trösch AG Swisslamex, Dow Corning and Nuova Oxidal for the material support and fabrication of specimens. Furthermore, the assistance and support of all TU Delft Stevin Laboratory members that contributed in preparing and conducting the tests is gratefully acknowledged.
Compliance with ethical standards
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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