Determination of a material law for two selected adhesives for adhesive point-fixings Simon Hollevoet & Kevin Verstraete Supervisors: prof. dr. ir.-arch. Jan Belis, ir. Jonas Dispersyn Abstract – More and more, bolted point-fixings of glass panes are left behind in favour of adhesive point fixings. This connection method has not only aesthetic benefits, but also highly reduces the occurring stress concentrations, thermal bridges and condensation problems. In this research, two adhesives (one flexible and one stiff) are considered. Material laws are calibrated to predict the occurring deformations of a verification setup. This setup consists of two steel cylinders, which are glued together with the considered adhesives. In order to check whether the material model is able to predict the deformations of the verification setup, the material model for each adhesive is implemented in a finite element approximation of this verification setup. The accuracy check consists of the comparison between the actual and the predicted relative displacement of the two steel cylinders. Keywords – Adhesive, point-fixing, finite element model, hyper elastic, strain energy potential, linear elastic I. INTRODUCTION The transition from bolted point-fixings to adhesive pointfixings leads to some remarkable benefits: • uniform transition of the occurring forces from the glass to the attachment points; • no micro cracks along the borehole; • reduction of the chance of occurrence of thermal bridges; • reduction of condensation problems; • the flat surface is easy for pre-treatment and adhesive bonding. Since the adhesives do not only need to take up the thermal expansion of the glass pane, but also need to have a certain strength to keep the glass pane in place, it is important to have the possibility to predict the behaviour of these materials. In order to predict this behaviour, material laws are calibrated with experimental data of tension, compression and shear tests. models are used. Therefore the adhesive is considered as incompressible. Tensile tests on dog bone samples lead to a Poisson ratio of 0.49, which leans close to the Poisson ratio of perfect incompressible materials (0.50). B. Material models Hyper elastic material models are based on the existence of a strain energy function W, which is a measure of the amount of energy in a certain material. It can be described by either statistical micromechanics of the molecular chains or by phenomenological material models. The first group of material laws are based on the modelling of polymer chains on micro level, e.g. 3-chain, 8-chain, fullnetwork, Flory-Erman and tube model. The second group of material laws has no theoretical background, e.g. Polynomial, Mooney-Rivlin, Neo-Hooke, Gent-Thomas, Hart-Smith, Ogden, Reduced Polynomial, Yeoh, Gent, PucciSaccomandi, Pamies-Lopez, Van der Waals. Strain energy function – The amount of energy is a function of the occurring stretches in the principle directions [2]. In the micromechanical material models, these stretches are modelled by relative chain stretches, while in phenomological material models the stretches are taken into account using strain invariants , and . For incompressible materials, is equal to 1. Polynomial model – The first phenomenological material model ever developed consists of an infinite sum of products of the strain invariants: (1) with the material parameters. Calibration – Using the following relations, the theoretical tension-compression and shear stresses can be calculated [3][4]. II. SOUDASEAL 270 HS A. Prior examination In order to decide what material model should be used to predict the behaviour of the Modified Silane (MS)-polymer, a Dynamic Mechanic Thermal Analysis (DMTA) is carried out [1]. This leads to a glass transition temperature of -64.74°C. Since the working temperature is much higher than this glass transition temperature, the adhesive is considered as a rubber. For the prediction of rubber materials, hyper elastic material S. Hollevoet and K. Verstraete are with the Faculty of Engineering and Architecture, Ghent University (UGent), Gent, Belgium. E-mail: [email protected], [email protected]. (2) (3) After partial derivation of the strain energy potential, the relations become function of the occurring stretches and material parameters. Using experimental data of tension, compression and shear tests, the theoretical formulations can be fitted to the experimental stress-stretch diagrams. This can be done by a non-linear least square fit. C. Experimental tests to obtain the material parameters In order to calibrate the material models, test data is required. Therefore several experimental tests on the adhesive as bulk material are carried out: • tensile tests on dog bone samples (ISO 527) [5]; • compression tests on massive cylinders (ISO 604) [6]; • Thick Adherend Shear Test (EN 14869-2) [7]. After processing the test data into stress-stretch diagrams, the calibration of the material models is done by a preprogrammed Matlab® procedure. After an extra cyclic loading procedure, it becomes clear that the adhesive is subjected to the non-ideal Mullins effect [8]. IV. PRODUCTION OF THE TEST SPECIMENS A. Moulds Both materials have to be mixed before being used for fabrication of the test specimens. The flexible adhesive is mixed with 5% water [10], since it hardens by moisture curing. The epoxy hardens by chemical curing, after both of the components are mixed together. The mixed adhesives are injected into PTFE moulds and stored in a climate chamber with a temperature of 21°C and relative humidity of 45%. B. Specimen dimensions Dog bones – According to ISO 527, the dog bones used in this research are of type B1. D. Different test data combinations Unlike stated in the literature, the material models are not only calibrated with as much as combined information as possible. The models are also calibrated using for example only test data from tensile tests or only shear tests. Following combinations of test data are possible: tension, compression, shear, tension-compression, tension-shear, compressionshear, tension-compression-shear. III. 3M SCOTCH WELD 9323 B/A A. Prior examination Also for the stiff two-component epoxy a DMTA is carried out. This time a glass transition temperature of 47.15 °C is obtained. Since the working temperature is lower than this value, the material is considered as crystalline. The behaviour is therefore approximated by a linear elastic model. The Poisson ratio is equal to 0.39 and the modulus of elasticity is equal to 2408.412 MPa, both obtained from tensile tests. The shear modulus is equal to 767.018 MPa (V-Notch) or 700.142 MPa (U-Notch). B. Material model Since the stiff epoxy is considered as a linear elastic material, only the linear elastic model following Hooke’s law is used. Calibration – Only the Poisson ratio and the modulus of elasticity are needed. These parameters are again obtained from experimental tests on bulk material. C. Experimental tests to obtain the material parameters For the calibration of the material models, only tensile tests are necessary. However, also compression and shear tests are carried out: • tensile tests on dog bones (ISO 527) [5]; • compression tests on massive cylinders (ISO 604) [6]; • Iosipescu Shear Test (D5379) [9]. After processing the test data, the relation between the modulus of elasticity, shear modulus and Poisson ratio is verified. A deviation of 10% occurs, which is acceptable to keep considering the epoxy as a linear elastic material. Also for this stiff adhesive, a cyclic loading procedure is carried out: the non-ideal Mullins effect is far less present [8]. Figure 1: Dog bones Cylinders – The massive cylinders have a height and diameter of respectively 15 and 30 mm. Figure 2: Massive cylinders Thick Adherend Shear Test – In order to eliminate moments in the adhesive, tiered aluminium substrates are used. Figure 3: Thick Adherend Shear Test specimen Iosipescu Shear Test – Pure shear on stiff bulk material needs an Iosipescu Shear Test setup, where V- or U-notched specimens is clamped into. Figure 4: (a) V- and U-Notch specimen (b) Iosipescu Shear Test setup C. Verification setup In order to validate the calibrated material models, an extra setup is considered. The test data will however not be used to calibrate the material model. It consists of two steel cylinders, glued together by both the flexible and stiff adhesive. Two variants are used, where firstly the contact surfaces are horizontal and secondly the contact surfaces placed under an angle of 45°. Figure 8: Speckle pattern on dog bone specimen Such a method is beneficial if several data has to be acquired out of one single test setup. After defining the area of interest, relative or absolute displacements, strain in different directions, virtual strain gauges, extensometers, etc. can be read out of the correlation software. Figure 5: Verification setup: (a) horizontal (b) 45° contact surface The thickness of the bonding layer of the flexible and stiff adhesive is equal to respectively 2 and 0.2 mm. Figure 6: Force-displacement diagrams – horizontal surface Figure 9: Sequence of DIC output images (strain) In this research, the DIC software is also used to calculate the occurring lateral contraction in order to determine the real specimen section and thus the real stress instead of the commonly used engineering stress. B. Why using DIC? The use of DIC is important if accurate test data has to be gathered, for example for the stress-strain behaviour of the considered adhesives. Especially for tensile test on the flexible dog bones, a big difference occurs when comparing the stress-strain diagram of DIC with the diagram based of the relative displacement of the testing machine clamps. After loading, the force-displacement diagrams of the setup with flexible adhesive show large variations. This is a consequence of the fact that the bonding layer not only fails due to cohesive failure, but also due to adhesive failure. Figure 10: Comparison strains: DIC vs. Tensile testing machine Figure 7: Combination of cohesive and adhesive failure (a) horizontal (b) 45° V. DIGITAL IMAGE CORRELATION A. Principle Digital Image Correlation (DIC) is a measurement method where occurring deformations of test specimens are calculated after applying a speckle pattern on it. It is a whole field measurement method. That means that, unlike the extensometer (considering the relative displacement of only two points), the deformations of a whole area of interest can be investigated. The measurement consists of taking photos of the specimen while the test is operating. After the test, the photos are implemented into correlation software, where the occurring deformations are calculated due to the relative movement of the speckles. The reason of the big difference is the fact that slip occurs in the clamps due to lateral contraction of the specimen. A comparable problem is encountered while testing the stiff adhesive verification setup. While the tensile testing machine reads out relatively big deformations of the clamps, DIC measures almost no relative displacement of the steel cylinders. It means that it is not the adhesive layer, but the steel bolt and cylinder, used for the placement of the setup between the clamps, that stretch. VI. FINITE ELEMENT MODEL A. Verification model In order to check the accuracy of the calibrated material models, both verification models are approached by corresponding Abaqus® finite element models. Optimal material model – Since the validation relies on only one verification setup, no optimal material model is proposed. However, after comparing all combinations and models, it seems that for the best results, shear tests always have to be carried out. Figure 11: Finite element approximation of the verification setup: (a) horizontal (b) 45° The flexible adhesive is modelled by C3D8H elements, while for the stiff adhesive C3D8 elements are used. To ensure that a regular mesh pattern consisting of Hex-elements is used, a regularly seeded square is provided in the middle of the adhesive layer. If not, automatic seeding, using Wigelements, would lead to irregular elements and a singular point in the middle of the adhesive layer. VII. VALIDATION OF THE MATERIAL MODELS A. Soudaseal 270 HS The theoretical and experimental relative displacements of the massive cylinders are compared to each other. The comparison is based on two evaluation criteria: • initial stiffness; • initial deformations. Since not only cohesive, but also adhesive failure occurs, the strongest verification setup is considered to validate the finite element model. The thought behind this is the fact that in the finite element model, neither cohesive nor adhesive failure is implemented. That means that the model represents an ideal situation. The only verification setup that comes close to that behaviour is the setup where the adhesive bond lasts as long as possible. This could also be the reason why the theoretical force-displacement diagrams are constantly linear, unlike the experimental diagrams where the first section is linear (no adhesive failure) and the second part becomes less steep. B. 3M Scotch Weld 9323 B/A Because the relative deformations of the steel cylinders of the verification setup are too small, the occurring noise on the on the measurements is bigger than the actual deformations. Because of that, no validation of the numerical model will be carried out. VIII. CONCLUSION Depending on the used combination of test data, different hyper elastic material models can be used to predict the behaviour of the flexible adhesive. The best calibration is obtained using (combined) data from shear tests. The modelling of the stiff adhesive could not be validated due to minor deformations. Both models are subjected to a non-ideal Mullins-effect (flexible adhesive to a greater extent). IX. FUTURE RESEARCH When carrying out similar investigations, it is important to prevent that adhesive failure occurs in the verification setup. At the same time, the finite element model has to be optimised by introducing break mechanisms of the adhesive and using cohesive elements. Also cyclic loading of the flexible adhesive can be investigated more in detail. X. ACKNOWLEDGEMENTS The authors would like to thank their supervisors for letting investigate this research subject. Also a special thanks to Zwick/Roell for the use of their tensile testing machine and dr. ir. Stijn Hertelé for the use and introduction to Digital Image Correlation. REFERENCES Figure 12: Predicted vs. practical deformation – horizontal Figure 13: Comparison predicted vs. practical deformations – 45° Dispersyn, J. (2014). Adhesive material models for structural glass applications. Rivlin, R. (1948). Large Elastic Deformations of Isotropic Materials. IV. Further Developments of the General Theory. Royal Society of London Philosophical Transactions Series A, 241, 379-397. Dias, V., Hechler, O., Odenbreit, C., Scholzen, F., & Ben Zineb, T. (2012). Develepment of material law for silicone to simulate structural adhesive connections. Paper presented at the Glasstec, Düsseldorf. Steinmann, P., Hossain, M., & Possart, G. (2012). Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data. Archive of Applied Mechanics, 82(9), 1183-1217. International Organization for Standardization , (1998). ISO 527-1,2: Plastic, determination of tensile properties. International Organization for Standardization, (2002). ISO 604: Determination of compressice properties. International Organization for Standardization, (2004). EN 14869-2: Structural adhesives. Determination of shear behaviour of structural bonds. Thick adherends shear test. Diani, J., Fayolle, B., Gilormini, P. (2009). A review on the Mullins effect. European Polymer Journal, 45, 601–612. ASTM. (2012). ASTM D5379: Standard Test Method for Shear Properties of Composite Materials by the V-Notched Beam Method. Dispersyn, J., Belis, J., Dias, V., & Odenbreit, C. (2013). Determination of the material properties of an epoxy and MS-polymer for adhesive point-fixings. Paper presented at the COST Action TU0905. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • − − − − − • • • • • • • • • • • • • • • • • •
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