Numerical Finite Element Models for the SSG Parameter Study
Based on a glass pane 1.25 m by 1.5 m in size, different configurations of monolithic and laminated glass units have been studied that exactly fulfill the design requirements of ETAG 002 with regard to bond sizing . Regarding laminated glass, both fully functional and totally degraded shear layer conditions are considered in this study as extreme cases. The fully functional shear layer assumes no shear strains of the interlayer (Kirchhoff plate theory, shear stiffness infinity), whereas the total degradation model allows relative slipping of the glass panes without shear stresses (panes decoupled in shear, shear stiffness zero). The first model is representative for low temperatures of the interlayer, and the second model is a limiting case for high temperatures. It is assumed that the behavior of insulating glass units in shear also is covered by these two extreme configurations of laminated glass, as the shear stiffness of the insulating sealant is between zero and infinity. Within the parametric studies, the glass thickness for laminated glass was varied from 6 mm to 8 mm to 10 mm, and for laminated glass two panes of 6 mm thickness are modeled, taking into account a shear layer with a thickness of 1.52 mm. For the load case of interest, a compressive constant surface load p was chosen in such a way that the sizing rule of ETAG 002 (Eq 6) was exactly fulfilled, leading to surface loads of 4.48 x 10~3 MPa for a bond width of 20 mm and 2.24 x 10~3 MPa for a bond width of 10 mm. Warping
deformed glass pane
-♦ inhomogenous loading
—► strengthening effect
Load carrying bonding —*• inhomogenous loading
was not applied, with the assumption that for low amplitudes linear superposition can be applied for the warping and unsteady loads, and thus the investigation of these phenomena is treated separately.
The numerical model is based on FEA (i. e., plate elements featuring linear elasticity for the glass units and solid elements featuring hyperelasticity for the adhesive, with both element types using quadratic shape functions). The supporting frame is assumed to be rigid, thus being considered as a boundary condition for the flexible structure. The assumption of total rigidity is a conservative approach typically leading to higher adhesive loads. A representation of the finite element model is given in Fig. 12 and Fig. 13. The meshing is
subjected to surface loads
FIG. 13—Composition of the finite element model.
Copyright by ASTM Int’l (all rights reserved); Tue May 6 12:07:08 EDT 2014 Downloaded/printed by
considered quite coarse, as the focus is put on mean or integral values within the adhesive bond.
For comparison with ETAG 002 and for a detailed assessment of the numerical results, the reaction loads of the adhesive are summed up element-wise in the bond width directions in order to get average values across the adhesive cross section for the distributed loads along the edges. In the corners, the reaction loads are related to the corner cross section as a natural extension of this approach. Afterward, the averaged stresses are plotted along the boundary edges, starting with the long side. Because of the symmetry conditions, it is sufficient to plot the stress values along one long edge and the adjacent short edge. The post-processing procedure for the stress values is sketched in Fig. 14.
Figure 15 presents results for both compressive and suction loads for a monolithic glass pane of 6 mm thickness and a bonding geometry of 20 mm bite and 9 mm thickness. This figure reveals two major issues; First, sign changes of the bonding stresses are observed in the corner areas, which is expected from plate theory. Second, the peak stress levels in the corner areas exceed the stress levels along the edges. Thus the assumption of trapezoidal stress distributions with vanishing strains in the corner zones, as incorporated in ETAG 002, is in complete contradiction to this numerical analysis. The remaining open issue is now the dependence of the averaged corner stresses with respect to various design variables.
For comparison purposes, Fig. 16 presents a typical stress distribution for a warped glass unit, assuming linear warping of the edges as shown in Fig. 3. For a consistent numerical approach taking into account large displacements, second order effects such as displacements in the x – and y-directions due to rotation along one of the diagonals are considered as well, in addition to the vertical displacement field and in-plane rotations. In addition to the stress distribution, Fig. 16 presents the stress distribution of ETAG 002 and a postulated tensile design stress limit of 0.014 MPa for permanent loads extrapolated from Table 1.
FIG. 15—Baseline results for compressive and suction loads; surface load of 4.48 x 10~3 MPa (glass unit: 1.5 m in length, 1.25 m in width, 6 mm in thickness; bonding: width — 20 mm, thickness — 9 mm).
The comparison with ETAG 002 shows that whereas the guideline predicts low stress levels in the corner region, warping leads to high stress levels in the corner area, leading to a wrong impression that interference between unsteady operational loads and warping loads might be low due to the missing corner peak loads in ETAG 002. The comparison with the extrapolated stress design limits demonstrates that even moderate warping amplitudes lead to obviously unacceptable stresses due to the assumed low stress limits. This issue underlines the need for improved silicone material knowledge with respect to creep and creep combined with operational loads in order to allow for higher design stress levels for cold bending techniques. In conclusion, the stress distribution field shows the following features:
• Peaks of the warping stress in the corner zones are obtained in Fig. 16 as expected due to the warping field.
• The warping stress field shows an almost vanishing interference with the ETAG 002 simplified (“trapezoidal") stress field, i. e., no or low coincidence of the warping stresses and the ETAG stresses.
• A significant interference of the warping stress field with the calculated stress field of Fig. 15 is obtained, as both stress fields show high levels in the corner zones.
Copyright by ASTM Int’l (all rights reserved); Tue May 6 12:07:08 EDT 2014
Rochester Institute Of Technology pursuant to License Agreement. No further reproductions authorized.
FIG. 16—Bond loading due to linear warping; bi-linear warping of 10 mm (glass unit: 1.5 min length, 1.25 m in width, 2 mm x 6 mm in thickness; bonding: width — 20 mm, thickness — 9 mm).
• Warping stress levels are lower for the selected warping amplitude than
the calculated wind load stress fields but are of a permanent nature.