This paper was first presented at GPD 2019 by Michael Härth, Stephen J Bennison, and Steven R Sauerbrunn.

The key to correctly simulating the behavior of laminated glass is to develop an accurate constitutive model for polymer interlayer. Such models should reflect polymer behavior as a function of temperature and load duration, so calculations can be made to reflect the design load conditions of interest. In this contribution, we propose several methods to determine the behavior of interlayer shear relaxation modulus.

The results of test methods based on dynamic mechanical analysis (shear, parallel plate geometry) are compared and compared. Two key findings were reviewed: 1) proper sample conditioning and preparation, and 2) minimized sample deformation during testing. We show that as long as these two issues are carefully managed, self-consistent results can be obtained from different test geometries. A key element of any evaluation plan is independent verification of results. Here, we checked the four-point bending test using laminated glass beams for such verification checks.

Many calculation tools and methods can now be used to simulate the deformation of laminated glass [1-7]. In fact, the development of such tools has played a key role in expanding the application range of laminated glass beyond its traditional function as safety glass, and as a structural element in exterior walls or buildings. Although the methods of these tools vary, from simple analytical approximations to detailed and complex finite element methods, accurate material properties are required. The polymers used in laminated glass exhibit complex viscoelastic behavior, in which the stiffness behavior is affected by the temperature and time scale of the load.

It has been 20 years since the first publication of research on the viscoelastic properties of PVB polymers and the related behavior of laminated glass made of such polymers [6, 7]. This work uses tensile mode dynamic mechanical analysis (DMA) to extract the potential shear relaxation modulus G(t) of PVB. Combining these characteristics into the finite element model proved to be able to predict the deformation of laminated glass under various geometric shapes and load conditions. These studies have been reused by other groups and have basically been verified [8].

Since this early work, we have seen the introduction of other polymer interlayers beyond the standard PVB developed for traditional impact glass applications. This interlayer covers a range of mechanical properties from the hardest structural polymers (such as ionomers) to the most flexible damping polymers (such as acoustically enhanced multilayer PVB). This complexity of material behavior brings additional challenges to accurately determining the shear relaxation modulus behavior required for design calculations.

We have seen some reported test results variability, which raises questions about the best way to characterize polymer interlayers [9]. In addition to this complexity, we have also seen a trend to promote the use of polymer storage shear modulus G'in the structural calculation of laminated glass. This is not correct. The storage shear modulus G'shows a higher value than the relaxed shear modulus G(t). Therefore, structural calculations using G'for the behavior of laminated glass will predict better performance than actual, because this method does not take into account the polymer relaxation during loading.

In this article, we introduced a method to determine the shear relaxation modulus G(t) of a polymer interlayer. We focus on several key issues: 1) proper sample conditioning and preparation, 2) minimization of sample deformation during testing, 3) TTS analysis method and accurate extraction of G(t), 4) using beam bending experiments to verify the results. We show that if these issues are carefully managed, self-consistent results for a specific category of sandwich can be obtained from different test geometries. In addition, we also provide a series of examples of the difference between G'and G(t) for PVB-based polymers.

In order to cover a wide range of rigidity of various sandwich products, this study investigated three commercial PVB sandwiches Trosifol® SC Monolayer, Trosifol® UltraClear and Trosifol® Extra Stiff. The main difference between these interlayers is the overall plasticizer content, which ranges from the high of the SC single layer, to the medium of UltraClear, to the low of Extra Stiff. The glass transition temperature (1 Hz, 3 K·min-1, linear range of deformation) was determined to be 20 °C for SC monolayer, 32 °C for UltraClear, and 47 °C for Extra Stiff.

The key issue for sample preparation is to ensure that the polymer film undergoes the same thermal process as the laminated glass manufacturing process. This results in the polymer reaching its correct equilibrium state before testing. For example, some polymers exhibit limited shrinkage during heating to autoclave temperature. If this happens during the test, the relevant signal (force) change is interpreted as a change in mechanical behavior. We have adopted two approaches to this request.

A film sample with a nominal thickness of 0.76 mm was laminated with a PET separator between PVB and glass, and exposed to a standard lamination process to remove the shrinkage and surface structure of PVB. The processed PVB film was then peeled from the PET separator, and a sample (8 mm diameter) was cut from the free-standing film, and then dried in a desiccator at 23°C for at least 48 hours before testing. This results in a moisture content of less than 0.2 wt.%, which improves the repeatability of the measurement and avoids the formation of bubbles at high DMA test temperatures.

The glass plate is exposed to standard lamination process. Subsequently, the laminated glass test sample (8 mm disc) was cut from the thin glass laminate using the water jet cutting method. A sample PVB film with a nominal thickness of 0.76 mm is laid between 0.7 mm "thin" glass plates and exposed to standard lamination processes. Then use water jet cutting to cut a laminated glass test sample (8 mm disc) from the thin glass laminate.

A series of test methods have been used to characterize the shear relaxation characteristics of several PVB-based sandwich materials.

The tests were performed in two different laboratories using two different test geometries and two different sample types.

Kuraray Troisdorf Germany: Freestanding polymer film sample

The dynamic-mechanical-analysis was performed in the plate/plate mode with Anton Paar MCR 302 rheometer. The specimen is loaded at 70 °C, and the metal mounting plate is moved toward the specimen at a constant speed (1 µm·s-1) until a normal force of 10 N is reached. Then set the normal force to 0.4 N, heat the rheometer to 120 °C, and then cool to the lowest test temperature of -20 °C. This procedure can achieve the required adhesion between the metal mounting plate and the PVB sample. The frequency sweep is performed in the linear range of deformation (maximum 0.1% strain) and a normal force of 0 N to avoid sample deformation during the measurement. The temperature varies between -20 °C and 105 °C in steps of 5 °C.

University of Delaware (UoD): Thin glass laminate samples

The dynamic-mechanical-analysis was performed in a plate/plate mode with TA Instruments rheometer. Please note that the thin glass laminate sample is glued to the mounting plate using high temperature epoxy. The sample is loaded at room temperature, and the normal force is maintained at 0 N during the entire test. Cool the sample to the lowest test temperature -20 °C and start the temperature frequency sweep. The frequency sweep is performed within the linear range of deformation (<0.1% strain) and a normal force of 0 N to avoid sample deformation during the measurement. The temperature varies between -20 °C and 105 °C in steps of 5 °C.

The dynamic-mechanical-analysis was also performed with Mettler Instruments DMA in shear mode. Please note that the thin glass laminate (8 mm disc) sample is glued to the mounting plate using high temperature epoxy. Load the sample into the sample holder at the lowest test temperature of -20 °C. The minimum clamping force is applied to the sample during installation to minimize polymer deformation during the test. A frequency sweep is performed in the linear range of deformation (< 0.1% strain), and the temperature is changed in steps of 5 °C between -20 °C and 105 °C.

A four-point bending test was performed to check the shear modulus evaluation results from the DMA test. These tests are carried out in two independent test laboratories: 1) Bundeswehr University Munich and 2) Friedman and Kirchner test laboratories. Testing included measuring the deflection of laminated glass beams and using finite element modeling to correlate load deflection behavior with shear modulus. A discussion on the applicability of this inverse method is given elsewhere [10].

Extract master curve and shear relaxation modulus

The time-temperature-superposition (TTS) analysis method has been fully reviewed [6-9]. Two key points to note: 1) use only horizontal movement to establish the master curve, 2) the evaluation of G(t) and the related linear viscoelastic spectrum was implemented after Baumgärtel and Winter [11].

Comparison of different methods and laboratories

Figure 1 shows an example of measurement comparison of Trosifol® Extra Stiff from two different DMA geometries, shear plates and parallel plates, and two different laboratories, Kuraray Troisdorf and the University of Delaware.

It can be seen from the results that the consistency of the two DMA methods is very good, and there is good consistency between the two laboratories.

Comparison of shear relaxation modulus G(t) and shear storage modulus G'

Figure 2 shows a comparison example of Trosifol® Extra Stiff G(t) and G'from parallel plate DMA measurement.

It can be seen that G'is always greater than G(t). The deviation of G'and G(t) represents the amount of polymer relaxation that occurs at a specific relaxation time (load duration) and temperature. Table 1 shows some G(t) and G'values ​​of Trosifol® ES, which further proves this point.

Figure 2 and Table 1 show that the difference between G(t) and G'can be quite large (up to 5 times in some cases). The deformation of the laminated glass plate depends on the shear relaxation modulus G(t) of the interlayer. If the interlayer shear storage modulus G'is used for calculation purposes, the prediction will be inaccurate. In fact, depending on the load duration, temperature, and the deviation between G(t) and G', the calculation may be seriously unconservative.

Verification using 4-point bending test

Ultimately, the shear characteristics derived from the described measurements need to be used to simulate the deformation of laminated glass. Therefore, we compared the DMA results with estimates of the shear modulus extracted from a 4-point bending test conducted at the Bundeswehr University in Munich.

It can be seen from Figure 3 that there is good agreement between the results of the 4-point bending test and the results of the DMA measurement. This comparison further supports the use of G(t) to calculate the deformation behavior of laminated glass.

We have shown that if several important guidelines are followed, the reliable and self-consistent shear relaxation modulus G(t) characteristic of polymers used in laminated glass can be measured. The results have also been verified based on the evaluation of the 4-point bending test. In addition, we have demonstrated the importance of using G(t) in calculating the deformation behavior of laminated glass.

The author thanks Dr. Michael Kraus (Bundeswehr University Munich) for performing the 4-point bending test and fruitful discussions.

1. JA Hooper, "On the Bending of Laminated Glass in Buildings", Int. J. Machinery. Science, Volume 15, Pages 309-23, (1973). 2. I. Calderone, PS Davies, SJ Bennison, H. Xiaokun and L. Gang "Effective Laminate Thickness for Laminated Glass Design", published on Glass Performance Days, Tampere, Finland, (2009). 3. L. Galuppi and G. Royer-Carfagni, "The effective thickness of laminated glass beams. A new expression through variational methods," Eng. Structure, Vol. 38, pp. 53-67, (2011). 4. L. Galuppi and G. Royer-Carfagni, "The Effective Thickness of Laminated Glass Panels", J. Mech. pad. Structure, Vol. 7, pp. 375-400, (2012). 5. L. Galuppi and G. Royer-Carfagni, "Practical Expression of Laminated Glass Design", Compos. Part B-English, Volume 45, Pages 1677-1688, (2013). 6. Bennison, SJ, Jagota, A. & Smith, CA, (1999) "Fracture of glass/polyvinyl butyral (Butacite®) laminates in biaxial failure", J. Am. Ceramics. Society, 82 [7] 1761-70. 7. Van Duser, A., Jagota, A., Bennison, SJ (1999) "Analysis of glass/polyvinyl butyral (Butacite®) laminates subjected to uniform pressure "Journal of Engineering Mechanics, ASCE, 125[4] 435-42. 8. Kuntsche J., Schuster M., Schneider J. and Langer S., "Viscoelastic Properties of Laminated Glass Interlayer Film-Theory and Experiment", 2015 Annual Glass Performance Day, pages 143-147. 9. Zhang P., Stevens W., Haldeman SV, Schimmelpenningh JC, "Measurement of Shear Modulus of Structural PVB Interlayer Film and prEN 16613", Glass Performance Day 2015, pages 148-52. 10. Shitanoki Y., Bennison SJ and Koike Y., "A practical and non-destructive method for determining the shear relaxation modulus behavior of laminated glass polymer interlayers", Polymer Testing 37 (2014) 59-67. 11. Baumgärtel M, Winter HH (1989). "Determine discrete relaxation and delay time spectra based on dynamic mechanical data." Acta Rheology 28:511519.

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