# Review of the Main Mechanical Testing Methods for Interlayer Characterization in Laminated Glass
## 3 Evaluation of Interlayer Properties According to EN 16613:2019
### Parametric Analyses  
Three glass thicknesses (5, 8, 10 mm), two interlayer thicknesses (0.76, 1.52 mm), and three different loading levels (600, 1150, 1800 N) were considered. Designation of the specimen is given according to the following ID tag, LG-5/8/10-076/152-060/115/180, where the first two capital letters 'LG' indicate the specimens made by laminated glass, the second serial numbers (5, 8, or 10) indicate the thickness of the glassply, the third serial numbers (076, 152) indicate the thickness of the interlayer, and the last numbers (060, 115, 180) indicate the different load levels. The numerical analyses allowed the displacements at midspan for each configuration to be evaluated (Figure 5). The results indicate, as expected, that the displacements decrease by increasing the glass or by decreasing the load. According to the standard procedure, the interlayer shear modulus \(G\) can be evaluated on the basis of the measured displacement at different load duration to allow designers to assess safety under different actions. Figure 5 shows that the thickness of the interlayer, has a strong influence on the response in case of sustained load, especially under a large load. However, a short time this difference is limited. Hence, the displacements at 86,400 s (24 h) were considered to evaluate the influence of the parameters under investigation. Table 4 reports for each case the deflection, the equivalent monolithic glass thickness (\(h_{mono}\)), the shear transfer coefficient \(\omega\), and the shear modulus of the interlayer \(G_{int}\). Figure 4: Validation of the numerical model. Figure 5: Midspan displacement vs. time curves. The equivalent monolithic glass thickness is a theoretical thickness of a monolithic glass that accounts for the deflection under load and is evaluated with the formula [24]:  
\[h_{mono}=\sqrt[3]{\frac{F\left(2L_{\mathrm{S}}^{3}+L_{\mathrm{B}}^{3}-3L_{ \mathrm{s}}L_{\mathrm{B}}^{2}\right)}{8E_{\mathrm{G}}bw}+\frac{60 QL_{S}^{4}}{384 E_{\mathrm{G}}bw}} \tag{1}\]  
where:  
\(F\) is the applied force (600, 1150, or 1800 N),  
\(Q\) is the self-weight of the LG plate in the form of a line load equal to 0.144 N/m,  
\(b\) is the width of the beam in the unit of m,  
\(w\) is the midspan deflection. The shear transfer coefficient \(\omega\) is evaluated with the relation:  
\[\omega=\frac{h_{mono}^{3}-\sum_{k}h_{k}^{3}}{12\sum_{k}\left(h_{k}h_{m,k}^{2}\right)} \tag{2}\]  
where \(h_{k}\), \(h_{m,k}\) are the thickness of the glass ply, and the distance between the centroid of the \(k\)-glass ply and the centroid of the LG ply, respectively. Furthermore, the interlayer shear modulus \(G\) can be evaluated by inverting the Wolfel-Bennison equation [5; 50; 51] as:  
\[\omega=\frac{1}{1+9.6\frac{h_{int}E_{\mathrm{S}}^{3}}{GL_{S}^{2}h_{m}^{2}}} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Specimen**} & **Glass** & **Interlayer** & **Load Level** & \(D_{86400}\) & \(h_{mono}\) & \(\omega\) & \(G_{int}\) \\  & **Thickness** & **[mm]** & **[N]** & **[mm]** & **[mm]** & **[mm]** & **[–]** & **[MPa]** \\ \hline LG5076060 & & & 600 & 7.28 & 9.5 & 0.60 & 1.93 \\ \hline LG5076115 & & & 1150 & 13.36 & 9.5 & 0.60 & 1.92 \\  
where \(h_{int}\) is the interlayer thickness, \(h_{nn}\) is the distance between the mid-plane of the glass plies, and \(I_{S}\) (moment of inertia per unit length) can be expressed as:  
\[I_{S}=\sum_{k}\left(h_{k}h_{m,k}^{2}\right)/\sum_{k}(h_{k}) \tag{4}\]  
Therefore, the shear modulus (\(G\)) can be determined through Equation (3), with the known parameters, as follows:  
\[G=\frac{9.6\omega h_{int}EI_{S}}{L_{S}^{2}h_{m}^{2}(1-\omega)} \tag{5}\]  
The results indicate that the stress level (for the considered range) does not influence the shear modulus, while it increases by increasing the thickness of the glass and by decreasing the thickness of the interlayer.