Hyperelastic Modeling

The unique capability offered by TSSA to support glass under dynamic and static loads via adhesive anchorage offers clear advantages for the design and aesthetics of the system, but more over it offers a technical advantage by elimi­nating concentrated stresses at drilled connections. Furthermore drilled con­nections within an insulating glass unit provide an additional potential path for moisture intrusion affecting the visual and thermal performance of the IG unit. Placements of adhesive anchors at closer intervals reducing the span between supports can allow thinner glass to be used which in turn may affect the dimen­sioning of the support structure installed behind the glazing. These are the types of scenarios that come about using this new anchorage system that lend them­selves to be validated with computer models to aid in optimizing designs. Soft­ware to analyze and predict behavior of hyperelastic materials is readily available that allows designers and engineers to understand the behavior of this silicone film adhesive when used in construction systems (see, for instance, [48]). For a comparative discussion of different material models used in the pre­diction of hyperelastic properties of silicone rubbers, such as Mooney-Rivlin, Yeoh, neo-Hookean, Arruda-Boyce, polynomial, and Ogden laws, see, for instance, various recently published reviews [49-52].

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Due to the increased strength and modulus of the TSSA material compared to classic structural silicones, additional applications are readily identified. The engineering community that uses finite element analysis to validate safety of structures prior to mockup testing has great interest in validating the behavior of systems anchored with TSSA.

Evaluation of the mechanical properties by uniaxial tension, planar tension (pure shear), and equal biaxial tension experiments are often used in the char­acterization of hyperelastic properties of silicone materials (see, for instance, [53-55]). Testing on TSSA was done in accordance with these test protocols to ascertain the material properties under slow cyclical loading with the intent of developing a data set that would satisfy the input requirements of mathematical materials models that are used in existing software for nonlinear finite element analysis once hysteresis effects are removed [54]. TSSA was characterized by these three tests using 1 mm thick film that was cured in an autoclave run in a regular production environment for curing PVB interlayers. The conditions in the autoclave ramped up to 12.4 bar (180 psi) and 135°C (275°F) over a period of 3.5 h. The 1 mm thick TSSA material was cured between polyester films. The testing was specified to pull the specimens five times each at a loading rate of

0. 01 strain/s (0.01 mm/mm/s) to an extension of 25, 50, 75, and 100%, respec­tively, before pulling the test specimen to destruction. The results of these cycli­cal tests in uniaxial tension, planar tension (pure shear), and equibiaxial tension are shown in Figs. 17-19.

FIG. 17—Results of cyclical uniaxial extension tests (engineering stress versus engi­neering strain).

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FIG. 18—Results of cyclical planar tension (pure shear) tests (engineering stress versus engineering strain).

The results of the cyclical tests indicate that, as the load is cycled, the shape of the stress-strain curve changes from concave-down to an S-shaped curve. In both cases, the engineering stress-strain curve increases monotonically. The peak stress for each cycle does not change, but the stress at each strain falls until it equalizes at 4-5 cycles. Furthermore, the cyclical tests indicate a failure point in the range of 7.5 MPa. The discrepancy between the failure load observed in the D412-type tests (see Fig. 5) and the failure load observed in the cyclical tests appears to be connected to the rate of loading; the cyclical tests were conducted at a rate of 0.01 strain/s, while the D412-type tests were con­ducted at a rate of 500 mm/min.

The findings of these three types of tests are further summarized in Fig. 20.

The experimental data were entered into a finite element model based on finite strain theory. Finite strain theory deals with situations where the unde­formed and deformed configurations of the continuum are significantly differ­ent and a clear distinction has to be made between them. This is commonly the case with elastomers. Elastomers that exhibit high strains in a uniaxial tension test have larger true stresses associated with the finite elements due to the fact that the test specimen cross section is changing with strain.

Therefore, it was acknowledged that the tensile engineering stress (force/ original unit area) and strain data would need to be converted to true stress

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FIG. 19—Results of cyclical equibiaxial tension tests (engineering stress versus engi­neering strain).

(force/actual unit area) and strain to provide a good comparison between gener­alized material testing and the results obtained in full-scale mockup of the bonded point fixing system. Without plastic flow occurring (i. e., strain being uniform along the specimen length), the engineering stress and strain can be converted to true stress and strain based on the following equations (assuming incompressibility of the material, i. e., a Poisson ratio of 0.5, which is an excel­lent approximation for silicone rubbers)

fft = ffe(1+£e) = ffek (4)

et = ln(1+£e)=ln k (5)

with rt as true stress, et as true strain, re as engineering stress, ee as engineering strain, and k as L/L0 the extension ratio.

Clift et al. [28] converted the data taken for TSSA in uniaxial tension to true stress versus strain by accounting for the changing in element sizes. Figure 21 shows an overlay of the engineering stress versus strain and true stress versus strain graphs as obtained from uniaxial tension testing.

Figure 22 shows the true stress distribution calculated based on finite strain theory in a model of the ASTM D412 type (dumbbell) specimen tested at 8.5 MPa engineering stress. As can be seen, significantly higher maximum true stress values occur in the thin section of the dumbbell than the 8.5 MPa meas­ured, with a maximum true stress of 31.9 MPa calculated.

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FIG. 20—Summary of equibiaxial, planar tension, and uniaxial tension in hyperelastic material testing (engineering stress versus engineering strain).

FIG. 21—Overlay of engineering stress versus strain and true stress versus strain graphs as obtained from uniaxial tension testing.

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FIG. 22—True stress distribution calculated based on finite strain theory in a model of the ASTM D412 type (dumbbell) specimen tested at 8.5 MPa engineering stress.

Visual observations in a full scale mockup testing of a glass pane held with TSSA bonded point circular supports showed a “crescent moon" shaped stress whitening in the TSSA at certain loads. The whitening was also visible in speci­mens subjected to destructive pull or to creep rupture tests. Since the stress

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FIG. 23—Stress whitening in actual mockup testing (left) and corresponding calculated stress distribution in TSSA material at whitening load state (note: rotated axis).

whitening appears to be a consistent response to a particular stress state, efforts were made to validate the stress whitening observed in the mockup scenario by using finite element modeling. Figure 23 shows the stress whitening observed in the actual mockup testing as well as the calculated stress distribution in the TSSA material at the whitening load state.

When the mockup was taken to destruction, cohesive failure of the TSSA was observed with a similar crescent moon shaped pattern as observed in the stress whitened bonded point support. Figure 24 shows the cohesive failure pat­tern in the TSSA at the point support as well as the calculated stress distribution in the TSSA material at failure load state.

FIG. 24—Cohesive failure pattern and calculated stress distribution in TSSA material at failure load state (note: rotated axis).

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Conclusions

The paper reports on the preliminary evaluation of a transparent structural sili­cone adhesive (TSSA), developed for point fixing in glazing.

The transparent film adhesive is a heat curing one-part material that shows strong bonding to glass, metals, ceramics, and even plastics typically without primer. While this evaluation is preliminary in nature and more detailed and comprehensive evaluations are planned or already underway, the following con­clusions can be drawn from the present work:

• The transparent structural silicone (film) adhesive (TSSA) combines high transparency, strong adhesion performance, thermal stability, and excellent weatherability.

• The TSSA has dynamic and static failure strengths substantially beyond what is observed for commercially available structural silicone materi­als today.

• Current work provides guidance in establishing a more detailed and comprehensive work program aimed at establishing the dynamic and static design strength of TSSA material.

• The stress whitening of the TSSA appears to be a consistent response to a particular stress state and is considered a positive feature, as it may allow derivation of dynamic design strength based on nondestructive testing as well as serve as an indicator of bonding strength in quality assurance testing.

• Hyperelastic modeling of TSSA bonded point supports is suitable for the analysis of the design and the explanation of performance.

Acknowledgment

The writers would like to thank their Japanese colleague, Kazuo Hirai, Dow Corning Toray Company, Ltd., for his contributions in the initial evaluation and the tensile creep rupture tests of the TSSA material.