Glass Belis, Bos & Louter (Eds.) Conference on Architectural and Structural Applications, Ghent University, September 2020. Copyright author. all rights reserved. ISBN 978-94-6366-296-3, https://doi.org/10.7480/cgc.7.4492

Christian Scherer Thomas Scherer Wolfgang Wittwer Thomas Schwarz Ernst Semar

HB Fuller | Kömmerling, Pirmasens, Germany

Since ancient times, people have had a keen interest in predicting the behavior of buildings. Now, to predict this behavior, we use experimental, increasingly time- and cost-effective computational simulations. Finite element analysis (FEA) is an increasingly popular method that has been firmly established in aviation and vehicle manufacturing for decades. In recent years, the use of numerical simulations to verify the use of adhesive bonding has grown significantly, especially in the development of exterior walls, where polymer materials (such as sealants or thermoplastic gaskets) have become more and more important.

This is partly driven by their expansion stress behavior, which is very different from the classic linear behavior of established materials such as aluminum, steel, or glass. The current work uses nonlinear material laws for FEA and demonstrates the behavior of sealant joints under various load conditions in multiple projects. The presented case studies show that the developed calculation method can be used to describe polymer materials very accurately, thereby simulating various loading conditions on glued components in a time-saving and money-saving way.

Glue connection is generally considered to be one of the most versatile connection technologies, and almost all technically available materials are connected using adhesive technology. Therefore, adhesives are increasingly used in structural applications due to versatility and continuous technological advancement, allowing the use of customized and application-oriented production techniques. Correspondingly, adhesive connections can be found in many applications, mainly in the field of structural glass and lightweight structures for connecting structural elements.

Even in the early stages of development and construction, for time and cost reasons, simulation is often used to shorten development time, identify weak points, and optimize the geometry of components and adhesive joints. Since the 1970s, finite element analysis (FEA) has been increasingly used in the numerical calculation of structural problems, and these problems cannot be solved accurately by analytical methods. The obvious advantage of FEA is that the mechanical properties of adhesives of almost any geometry can be determined under different load conditions.

The method can also determine the stress and strain distribution in the composite structure caused by the applied force or displacement. The accuracy of design calculations depends on the effectiveness of the material models used to describe the deformation behavior of adhesives and adhesive surfaces in the analysis, as well as the availability of material parameters applicable to these models.

Many adhesives, especially elastomers, exhibit complex stress-strain behavior due to their three-dimensional network structure and quasi-static stress, indicating a significant difference between the tensile and compressive load ranges. This behavior can no longer be described by linear calculation methods; instead, non-linear calculation methods must be developed and used. This article describes the development of nonlinear material models for describing polymer materials and their applications using various examples.

Generally, the linear material law can only be used to describe the material behavior of polymer materials relatively inaccurately. This depends on the loading speed, the type of loading, the temperature, and the thermomechanical history of the material or components made from it. At the same time, the requirements for calculation accuracy tend to increase. The parameterization and even development of nonlinear material models that describe a large number of these properties are very time-consuming and therefore costly.

To be able to work efficiently in this environment, the required accuracy must be determined before calculations. For this reason, it may be useful to perform relatively simple calculations to obtain basic knowledge using less complex material models in the early concept stage. In contrast, simpler models often fail to provide the necessary accuracy for detailed considerations. Figure 1 illustrates the different levels of accuracy and workload.

When choosing a suitable test method, it is necessary to know the load to be mapped and the required accuracy as accurately as possible so that the appropriate test or test setup can be selected. For the parameterization of nonlinear material models, it is usually necessary to use multiple load modes for testing, and these tests may also be performed at different temperatures and speeds. Figure 2 shows an example of test options for parameterization of a hyperelastic material model. The experiment spans the possible deformation fields (gray) in the second graph of the first invariant of the deformation tensor (see Baaser, H. 2010, Scherer, T. 2014, Weiß, R., Osen, E., and Basser Er, H. 2010).

The test selection shown in Figure 2 is just an example, and further or different tests can be imagined (see for example Drass, M., Schwind, G., Schneider, J. and Kolling, S. 2017). Then verify the material model that is inversely parameterized by the measured force-deformation curve, so that it can evaluate and verify its predictability in practical applications. This is usually done by comparing the measured data of the test with the most complex deformation state possible with calculations based on a parametric model (for example in Scherer, T. 2014).

The following examples illustrate the basic process and briefly describe the results obtained. The goal is to outline the possibilities as broadly as possible, not to describe each example in detail.

For example, here you want to determine the size of an L-shaped adhesive joint (two-component structural silicone adhesive) that fixes a glass plate (thickness d = 4 mm) in an aluminum frame. Such adhesive joints are common in solar collectors, for example. The size of this joint geometry is not based on international standards, such as covering EOTA ETAG 002 (EOTA-European Technical Certification Organization. 2012). The size of the pane and the shape of the L-shaped joint are shown in Figure 3. In this example, a wind load condition with a suction force of 2400 Pa is calculated. The purpose is to evaluate the load on the adhesive.

In this application, the adhesive uses a non-linear material model, while the substrate material uses a linear elastic method. This model is described in more detail in Figure 4.

In addition to the selected material model, the design dimensions suitable for evaluating the adhesive load must also be specified here. For this reason, the design strain energy is calculated according to the design value of EOTA ETAG 002. It can only be used for pure tensile or tensile shear load, and then it is suitable for multiaxial stress and strain conditions. This procedure is described in more detail in (Scherer, T., Wittwer, W., Scherer, C., and Semar, E. 2018). This gives the design value described in Equation 1.

Use Udes to design strain energy.

The calculation result of strain energy density is shown below (Figure 5).

Shows the parts passing through the long and short sides and the corners of the module. The results clearly indicate the critical stress area in the adhesive. They occur where the relatively thin thickness of the adhesive layer connecting the two substrates and the load caused by the large obstacle to lateral expansion have a high hydrostatic ratio. This model provides valuable insights for the dimensioning and geometric optimization of the components.

This example shows calculations for an insulating glass unit that is initially flat, and then bent when installed in an aluminum base structure in order to be able to achieve a curved shape. The demand for such applications is currently growing strongly because it allows the building envelope to be visually very elegant and complex. An example of such an application is the biaxial curved roof of the Chadstone shopping mall in Melbourne, Australia. The roof can be seen in Figure 6. Check the load on the edge of the hollow glass unit.

The non-linear material model is used for the secondary seal and the main seal (Ködispace 4SG in the first model and Kömmerling GD 115 in the second model) to compare and calculate two alternative insulating glass structures. The glass plate is mapped linearly and elastically. These models are described in more detail in Figures 7 and 8.

The bending results in shear deformation of the edge bond, which is transferred to the edge bond through the frame and glass plate. Figure 9 shows the shear deformation at the edge joint. The results clearly show the advantages of Ködispace 4SG under such load conditions.

Due to the significant increase in layer thickness, the deformation (here, shear deformation) is distributed throughout the cross section, and the maximum deformation is almost 10 times smaller. These results are described in more detail in (Scherer, C., Scherer, T., Semar, E., and Wittwer, W. 2019), which also considers the load in the aluminum gasket.

In the production of insulating glass, the newly produced units are stacked into packages immediately after production, slightly inclined to the vertical direction. Part of the weight of the above unit is applied to the lowest IG unit. It should be estimated what deformation occurs at the edge junction. Special consideration should be given to the behavior of units with thermoplastic gaskets.

Here, an IG unit of 1000 mm x 2000 mm is considered, and the window space is 16 mm.

The load conditions described are very complex and are affected by multiple influences, some of which will change over time. Three basic components contribute to the overall stiffness of the IG unit: the contribution of the auxiliary seal, which increases as it solidifies after the manufacturing process, the contribution of the viscoelastic behavior of the thermoplastic gasket, which decreases over time, and the sealing Filled with gas. The following force balance applies (see Figure 10):

Rheometer measurements are used to determine the increase in stiffness of the cured secondary sealant over time. Follow the same procedure for thermoplastic spacers. The force ratio of enclosed air or enclosed gas is calculated according to the ideal gas law. This gives the force as a function of time and strain, as shown in Figure 11.

The compression of the entire edge combination can be calculated using this. As mentioned earlier, the expected accuracy here is within the rough estimate range in order to better understand the entire system.

Using the assumptions made in 5.2, the time-dependent strain of each component can be calculated, thereby calculating the deformation of the entire IGU. These results are shown in Figure 12.

One chooses the highest compression after 3.6 minutes and then relaxes over time. The results showed that the compression that occurred was generally very slight. For the manufacture of the unit, this means that it can still be stacked during curing without affecting the dimensional accuracy of the IG unit. Figure 13 shows the force share over time.

Surprisingly, so far, the largest part of the load-bearing capacity comes from the enclosed gas, so the time effect of the secondary sealant and the thermoplastic separator plays a secondary role. Although the accuracy of the results cannot be compared with the results described in Chapters 3 and 4, they are very suitable for understanding the complex behavior of load cases in a sufficiently accurate manner.

Ködistruct LG is a polyurethane-based composite resin used in the production of glass laminates. Compared with monolithic glass panels, its excellent mechanical properties can reduce weight and can produce stable cold-formed laminates. Technical modeling requires a material law that accurately describes the deformation of the laminate according to load, time, and temperature. This material law is ultimately a prerequisite for granting German National Technical Approval (abZ) for laminates made of the above-mentioned liquid composite materials.

At first glance, relaxation experiments at different temperatures show very different behaviors (Figure 14). The progressive creep behavior of laminates was observed to end at a fixed limit at higher temperatures, while progressive creep was recorded at lower temperatures.

In order to determine the Arrhenius activation barrier EA, the thermodynamic properties were determined by dynamic thermodynamic analysis (DMTA). The N device was performed on the Eplexor 100 in a tear mode at six different frequencies f (0.25; 0.5; 1; 3; 10 and 25 Hz) And the complex elastic modulus E* and loss factor tan δ results are recorded and plotted (see Figure 15).

If the frequency is regarded as the velocity in the Arrhenius equation, the maximum tan (δ) is evaluated as the glass transition temperature Tg- at each frequency f. The Arrhenius diagram (see Figure 16) provides the Arrhenius activation energy EA.

The time-temperature superposition factor can be calculated using equation (3).

The temperature correction of the entropy elastic part of the shear modulus (G∞) comes from the measurement results at higher temperatures. Convert to other temperatures in the following ways:

Using these factors, the measured relaxation (creep) curves can be combined into a continuous master curve (see Figure 17).

The main curve can be well approximated by the Weibull function.

Based on these relationships, it is possible to calculate the shear modulus of the composite layer, which is also effective in a wide range of time and temperature.

Using the rheological material parameters of these viscoelastic finite element models, experimental results with good accuracy can be calculated with actual measurement results. Based on this model, as long as the material is simple in thermorheology and thermoset, excellent long-term predictions can be derived from laboratory-scale short-term tests (see also Wittwer, W., Schwarz, T. 2013 and Wittwer, W ., Schwarz, T. 2016).

Using various examples, it is shown that the non-linear calculation method can be used to describe polymer materials very accurately, which means that various load conditions can be simulated on the adhesive component at low cost. For example, a hyperelastic material model was proposed to study the load behavior of L-shaped silicone joints in solar collectors-for numerical simulation. In addition, FEA impressively demonstrates that the deformation of the flexible thermoplastic gasket is reduced compared to the traditional rigid box profile installed in the curved insulating glass unit.

The development of non-linear calculation methods for adhesives allows the description of complex load situations in application-related fields, such as stacking new sealed insulating glass with uncured edge bonding, and excellent long-term prediction of deformation. The behavior of glass laminates depends on different Load and effect. In the future, calculations and simulations will be more precise and will replace increasingly complex component testing, making them an integral part of adhesive technology.

Baaser, H.: Simulationsmodelle für Elastomere. ATZ -Automobiltechnische Zeitschrift, Ausgabe 05/2010, 364–369(2010) Drass, M., Schwind, G., Schneider, J., Kolling, S.: Adhesive connection in glass structures-Part 1. Thin layer experiments and analysis of structural silica gel. Glass Struct Eng 9, 3, 140(2017) EOTA-European Technical Certification Organization. ETAG 002-European Technical Approval Guide for Structural Sealant Glass Kit (SSGK), Brussels (2012) Scherer, C., Scherer, T., Semar, E. and Wittwer, W.: Ködispace 4SG, der Schlüssel für energieeffiziente kaltegebogene structure -Glass-Fasaden. In Glasbau 2019, B. Weller and S. Tasche, Eds., 439–449 (2019) Scherer, T.: Werkstoffspezifisches Spannungs-Dehnungs-Verhalten und Grenzen der Beanspruchbarkeit elastischer Klebungen, Technische 10 Wittcher, W. . And Semar, E.: What are the dimensions of elastic bonded joints with complex geometries? – System methods other than ETAG 002. In the Challenge Glass Conference Proceedings, Vol. 6. Pages 369-380 (2018). Weiß, R., Osen, E. and Baaser, H.: FEM–Simulation von Elastomerbauteilen. ATZ -Automobiltechnische Zeitschrift, Vol. 103, No. 3, 242–247 (2010) Wittwer, W., Schwarz, T.: Material laws for shear load and creep behavior of glass laminates. COST Action TU0905, Interim Conference on Structural Glass-Belis, Louter & Mocibob (Eds) © 2013 Taylor & Francis Group, London, ISBN 978-1-138-00044-5(2013) Wittwer, W., Schwarz, T .: A deterministic mechanical model based on the laws of physical materials for glass laminates. Engineering transparency (2016)

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