The problem of a failure criterion for glass-metal adhesive bonds
5
0
0
Hele tekst
(2) The Problem of a Failure Criterion for GlassMetal Adhesive Bonds Dieter Callewaert a), Arno Van Hulle a) , Jan Belis a), Freek Bos a), Jonas Dispersyn a), Bas Out b) a). Ghent University Laboratory for Research on Structural Models, Department of Structural Engineering, Technologiepark-Zwijnaarde 904, B-9052 Ghent, Belgium b). Delft University of Technology Adhesion Institute, PO box 5058, Kluyverweg 1, 2629 HS Delft, 2600 GB Delft, The Netherlands. Keywords 1=Adhesive. 2=Failure criterion. Bonding and Point Fixing in Glass. Abstract Although there is an increasing desire to apply structural adhesive bonds in glass constructions, the lack of a reliable failure criterion is a major obstacle. Since the average overlap shear strength values normally provided cannot be applied as a general limit for arbitrary adhesive bond geometries, extensive testing has to be performed on any new design to ensure its structural performance and safety. Not only the building industry, also maritime, aeronautical and car industries are struggling with this issue. To supply a contribution, this paper provides a numerical analysis of the stress distributions in an adhesive layer during a single lap shear test as was performed at Ghent University. Firstly, an appropriate mesh and element type was chosen after which the influence of different geometries on the peak shear stress was investigated. Additionally, simulations with different stiffness levels for the adhesive were performed. From the numerical analyses, it could be concluded that the impact of the thickness is most important. This study is part of an extensive, two-year research project into structural glass-metal adhesive bonds, run by Ghent University in cooperation with the Adhesion Institute of the TU Delft.. Introduction – Glass-metal adhesive bonds Adhesively bonded connections are becoming increasingly popular. In many application fields, such as aeronautics, automotive, shipbuilding and the building industry, this connection type gains interest above more traditional connection methods such as bolting and welding. The main advantages are the high construction efficiency and the favourable stress distributions. The more evenly spread stresses are especially well-suited for use with glass elements in structural applications. By avoiding the weakening of the glass pane due to drilling, local stress peaks can be avoided in the brittle 654. Monday-saturday-sunday_UUSI.indd 654. 3=Lap shear. 4=FE Analysis. material. Additional advantages can be the formation of a watertight joint between elements that can be made from different materials and the damping of vibrations through the adhesive material, which is relatively soft compared to glass and metal. The increasing structural requirements for bonded connections demand a good understanding of the mechanical behaviour of the adhesives. Well-defined test methods are becoming essential to determine the actual stiffness and strength of the many different adhesive materials. A correct interpretation and extrapolation of the test results is imperative. Therefore, knowledge must be acquired about the stress distributions and deformations across the volume of the adhesive. From this, a failure criterion can be set up, independent of the geometry of the bond and the applied loads.. Single Lap shear test A common test method for adhesives is a single or double tensile lap shear test. A shear force is introduced in an adhesive layer by applying a tensile force on two bonded substrates. Within the TEchnology TRAnsfer (TETRA) research project: “Building with Glass and Adhesives”, this test method was selected to select the most promising adhesives out of 32 different materials apparently suitable for glass to metal bonding. The results of this broad screening are concisely summarised by Belis et al. in an accompanying paper [1]. In the latter, a uniform shear stress across the entire surface was assumed to calculate the maximal failure stress from the measured force for a straightforward comparison of the different materials. In this paper, the stress distribution is investigated more in detail. Figure 1 displays a test sample clamped in the universal electromechanical test machine. To avoid early glass failure, a customised clamp to introduce a compressive force in the glass substrate was developed. The aluminium substrate on the other. 5=Linear elastic. Figure 1: Test specimen in the test machine to be subjected to lap shear. hand, was clamped directly and was loaded with a tensile force. Because of this non standard load introduction, existing analytical models to approximate the shear stress distribution in the adhesive are not applicable. For example, the model developed by Volkersen [2], which is generally accepted as a relatively easy calculation tool which takes into account the stiffness of the substrates, is only applicable for a lap shear with tensile forces on both substrates. Therefore, the stress distribution in the test samples is further analysed with a finite element model in Abaqus. Because of the complexity of the subject, these simulations are limited to linear calculations with pure elastic materials.. Numerical analysis Boundary conditions The boundary conditions of the customised test setup were simplified (see Figure 2) and implemented in the finite element model (see Figure 3). Additionally, only half of the test sample was simulated, based on the symmetry along the longitudinal axis, in order to minimise the calculation time. Therefore, the horizontal displacements perpendicular to the surface were prevented on one side of the sample. GLASS PERFORMANCE DAYS 2011 | www.gpd.fi. 18.1.2012 09:50:52.
(3) Figure 2: Simplified boundary conditions of the performed lap shear test. Figure 4: Indication of the section (left) and path (right) for the stress distributions of the next figures. Figure 3: Finite element model with representation of the boundary conditions. Figure 5: Shear stress across the adhesive layer with a general mesh size of 1 mm (left) and 0.3 mm (right). 0,20 0,18 0,16 0,14 0,12 0,10 0,08 0,06 0,04 0,02 0,00. size=1 size=0.3 re$ned 5. 10. 15. 0,20 0,18 0,16 0,14 0,12 0,10 0,08 0,06 0,04 0,02 0,00. size=1 size=0.3 re$ned. 20. 0. 0,01. Figure 8: Shear stress for different element types. 0,20 0,15 0,10. avg=75% avg=0%. 0,05 0,00 0. 5. 10. 15. Mesh size Firstly, a mesh study was performed because the stress output of a FE model is highly influenced by the chosen mesh and element type. If a general mesh size is implemented over the adhesive layer, the peak shear stresses seem to appear in the centre of the material. This result is presented in Figure 5, where two different sizes yield almost identical results. The shown stresses were selected at the section depicted in Figure 4 (left). This stress distribution conflicts with the analytic models, which all predict peak values of the shear. Monday-saturday-sunday_UUSI.indd 655. 0,04. 0,05. 20. 0,15 0,10. Element type Secondly, the element type for the adhesive layer was varied to retrieve a type of element which returns a plausible stress distribution with an acceptable computing time. Linear (C3D8) and quadratic (C3D20) volumetric bricks were used, both regular and with reduced integration points (C3D8R and C3D20R. avg=75% avg=0%. 0,05 0,00 -0,01. stress near the free edges. Therefore, a mesh refinement was implemented in these regions, which revealed an important peak shear stress very close to the free edge (see Figure 6). The shear stresses across the path indicated in Figure 4 (right) are summarised in Figure 7. To distinctly indicate the difference, a detail of the first part of the graph is presented as well.. GLASS PERFORMANCE DAYS 2011 | www.gpd.fi. 0,03. 0,20. Distance across overlap length [mm]. and a width of only 12.5 mm instead of 25 mm was simulated. A uniform pressure load was applied on the glass surface to approximate the actual loading case.. 0,02. Distance across overlap length [mm]. Shear stress [N/mm!]. Shear stress [N/mm!]. Distance across overlap length [mm]. 0,01. 0,03. 0,05. Distance across overlap length [mm]. respectively). For the linear elements, brick elements with incompatible modes (C3D8I) and hybrid brick elements with incompatible modes (C3D8IH) were also simulated. Figure 8 represents the results of these six different element types. It can be seen that only the C3D8R and C3D8IH volumetric elements show a local peak near the edge, followed by some lower values at the free edge. Because this coincides with the path that was expected theoretically, the other element types were no further considered. Because the stress distribution and the computation time between the two remaining element types was not significant, C3D8IH elements were preferred based on the experience with this element type in finite element models for laminated. Bonding and Point Fixing in Glass. 0. Shear stress [N/mm]. Figure 7: Shear stress along the path represented in Fig. 4 (right) for different meshes. Shear stress [N/mm]. Figure 6: Shear stress across the adhesive layer with significant mesh refinement at the edges: entire section (left) and detail of lower left corner (right). 655. 18.1.2012 09:50:52.
(4) 0,15 0,10. avg=75% avg=0%. 0,05 0,00 0. 5. 10. 15. 0,20. Shear stress [N/mm!]. Shear stress [N/mm!]. 0,20. 20. 0,15 0,10. avg=75% avg=0%. 0,05 0,00 -0,01. 0,01. 1,00 0,80 L=5. 0,60. L=10. 0,40. L=20. 0,20. L=30. 0,00. L=40 0. 10. 20. 30. 0,80 L=5. 0,60. L=10. 0,40. L=20. 0,20. L=30 L=40. 0,00. 40. 0. 0,01. Shear stress [N/mm]. Shear stress [N/mm]. 0,2 L=5. 0,15. L=10. 0,1. L=20. 0,05. L=30. 0. L=40 20. 0,03. 0,04. 0,05. 30. 0,2 L=5. 0,15. L=10. 0,1. L=20. 0,05. L=30 L=40. 0. 40. 0. 0,01. 0,02. 0,03. 0,04. 0,05. Distance across overlap length [mm]. . . . . . . . . .
(5)
(6) . . . . . . . . . . . . . . . Figure 11: Shear stress for different overlap lengths with proportional load. . . Figure 12: Shear stress for different thicknesses of the adhesive layer. . . Figure 10: Shear stress for different overlap lengths with identical load. 0,25. Distance across overlap length [mm].
(7)
(8) . 0,02. Distance across overlap length [mm]. 0,25. 10. Figure 9: Averaged and actually calculated shear stress. 0,05. 1,00. Distance across overlap length [mm]. 0. 0,03. Distance across overlap length [mm]. Shear stress [N/mm]. Shear stress [N/mm]. Distance across overlap length [mm]. . . . . .
(9)
(10) .
(11)
(12) .
(13) . . Figure 13: Maximal occurring shear stress in function of the overlap length (left) and the adhesive thickness (right). . . . . . . . . . 0,25 0,20 0,15 E=1. 0,10. E=10. 0,05. E=100. 0,00 0. 5. 10. 15. Distance across the overlap length [mm]. glass. These hybrid brick elements with incompatible modes are often used for the visco-elastic interlayer materials [3] [4], which have in general a mechanical stiffness comparable with common adhesive materials and are also usually loaded in shear. 656. Monday-saturday-sunday_UUSI.indd 656. 20. Shear stress [N/mm!]. . Shear stress [N/mm!]. Bonding and Point Fixing in Glass. . 0,25 0,20 0,15 E=1. 0,10. E=10. 0,05. E=100. 0,00 -0,01. 0,01. 0,03. 0,05. Distance across the overlap length [mm]. Average stiffness values In Abaqus, stresses in nodes shared between two elements are generally shown as an averaged output from the multiple elements that share the nodes (typically Avg. 75% as can be seen in. Figure 14: Shear stress for different stiffness levels of the adhesive layer. Figures 5 and 6). As a result, the given results do not show the stress peak that is actually calculated at the integration points. To make this distinction visible, the averaged and actually calculated shear stresses are combined in the same graph and displayed in Figure 9.. GLASS PERFORMANCE DAYS 2011 | www.gpd.fi. 18.1.2012 09:50:54.
(14) Geometry of the adhesive layer The influence of the overlap length on the stress peak value was investigated by simulating different geometries. Figure 10 displays the numerically calculated shear stresses for lap shear tests with several overlap lengths between 5 mm and 40 mm. Evidently, the stresses decreased when increasing the overlap length, the load being transferred through an increasing section. Therefore, the stresses are also simulated for a load which is proportional to the overlap length. This is represented in Figure 11. Additionally, a variation of the thickness of the adhesive layer was investigated. Different thicknesses between 0.3 mm and 10 mm were simulated of which the resulting shear stresses are summarized in figure 12. A major influence could be observed. The influence of these geometrical changes on the maximal peak shear stress is displayed in Figure 13. For the performed linear simulations, the influence of the overlap length is less pronounced than the influence of the adhesive thickness.. Stiffness of the adhesive material Finally, the influence of the stiffness of the adhesive layer was looked at. Therefore, the Young’s modulus of the. adhesive material was varied between 1 N/mm² and 100 N/mm². Figure 14 displays the numerically calculated shear stresses for these cases. This indicates that the influence is noticeable but rather limited compared to the impact of the adhesive thickness.. to linear calculations with pure elastic materials. For ductile materials, the maximal strain should be investigated as well to form the basis of a failure criterion. For brittle adhesives on the other hand, failure mechanics should be looked at with e.g. energy release rates.. Summary. Acknowledgements. The boundary conditions of executed single lap shear experiments were implemented in a finite element model. After determining the optimal mesh size and element type, the influence of a changing geometry or adhesive stiffness could be investigated.. This research was supported by the Agency for Innovation by Science and Technology in Flanders (IWT – TETRA 090170) and by the following organisations (in alphabetical order): 3M, Bureau Bouwtechniek, Delo, De Witte Aluminiumconstructies, Dow Corning, DuPont de Nemours, Federatie van Aluminiumconstructeurs, Huntsman, Kuraray, Lerobel, Lord, Miniflat, Proviron, Sadef, Scheldebouw, Sigu, Sika, Soudal and Viba. Furthermore, the feedback of the Belgian Building Research Instititute, Clusta, Oosterlinck Consulting & Development and Seco is gratefully acknowledged.. The main conclusions are: • The influence of the overlap length on the maximal occurring shear stress level is rather limited for a proportional load • The maximal shear stress increases for stiffer adhesive materials • The overlap thickness has a major influence on the peak shear stress. References The numerical simulations will be further evaluated with analytical models for single lap shear tests and compared with other loading conditions, such as thick adherend tests and tensile experiments, as described in [5]. This should provide a better evaluation criterion of experimental results compared to the oversimplifying assumption of a uniform stress distribution. Using finite element analysis, it is also possible to calculate more complex stress criteria, such as the Von Mises stresses and the Tresca stresses relatively easy. With these, it is possible to compose an even more reliable strength criterion out of a series experiments in which the adhesive failed cohesively. Naturally, it is then necessary to evaluate the calculation of an application on the same basis as the test results. Finally, it must be emphasised that the presented simulations are restricted. GLASS PERFORMANCE DAYS 2011 | www.gpd.fi. Monday-saturday-sunday_UUSI.indd 657. [1] Belis, J, Van Hulle, A, Out, B, Bos, F, Callewaert, D, Poulis, H. Broad screening of adhesives for glass-metal bonds, Proceedings of Glass Performance Days 2011, Tampere, June 2011 (this issue). [2] Volkersen, O. Die Nietkraftverteilung in zugbeanspruchten Nietverbindungen mit konstanten Laschenquerschnitten, Luftfahrtforschung 15, 1938, pp. 41-47. [3] Van Duser, A, Jagota, A, Bennison S J. Analysis of Glass/Polyvinyl Butyral Laminates Sibjected to Uniform Pressure. Journal of Engineering Mechanics, April 1999, pp. 435-442. [4] D’Haene, P, Savineau, G. Mechanical properties of laminated safety glass – FEM Study. Proceedings of Glass Performance Days 2007, Tampere, June 2007, pp. 594-598. [5] Van Hulle, A, Belis, J, Callewaert, D, Scheerlinck, L, Out, B. Development of structural adhesive point-fixings, Proceedings of Glass Performance Days 2011, Tampere, June 2011 (this issue). Bonding and Point Fixing in Glass. It is clear that the difference between the stress level in two adjacent elements is substantial. For the non-averaged stress, the values for the nodes at both sides of the same element are quasi-identical, but the values from the different elements at the same node can vary significantly. In this particular case, the calculated shear stress in the second element is 0.184 N/mm², while the maximal averaged shear stress is only 0.179 N/mm². Especially in this case, where the maximal peak stress is very important to define a strength criteria, this difference can’t be disregarded.. 657. 18.1.2012 09:51:00.
(15)
GERELATEERDE DOCUMENTEN
Therefore, background information is provided for fluid dynamics, normal human and chicken heart development, cardiac malformations, cardiac and vitelline blood flow, and the
Diagram showing a semi-quantitative representation of expression levels of KLF2, ET-1 and NOS-3 in the endothelium/endocardium of the sinus venosus (SV), atrioventricular canal
Thus, by ligating the right lateral vitelline vein blood flow patterns through the heart shift, resulting in a change in shear stress and in alterations of gene expression, which
Effects of ET-1, selective ETA (BQ-123), ETB (BQ-788), and non-selective endothelin receptor antagonist (PD145065) infusion on dorsal aortic blood flow (a), stroke volume (b),
Furthermore, μPIV is more sensitive than Doppler ultrasound, since changes in heart rate, volume flow rate, and shear stress in the vitelline veins were registered by μPIV, and
We demonstrate the presence of monocilia on endocardial-endothelial cells in areas of low shear stress and postulate that they are immotile primary cilia, which function as
The gene expression patterns of endothelin-1 (ET-1), lung Krüppel-like factor (KLF2) and endothelial nitric oxide synthase (NOS-3) during normal chicken cardiovascular development
Furthermore, ET-1, endothelin-converting enzyme-1 (ECE-1) and endothelin-B receptor (ETB) mRNA were shown to be expressed in the vitelline vessels, whereas endothelin-A receptor
