# Prediction of Pre- and Post-Breakage Behavior of Laminated Glass Using a Phase-Field Damage Model
## 2 Experiments  
The concept of sacrificial-glass-ply design [12] was adopted in [10] to propose two specific geometries. In such a case, the outer glass layers are made thinner as they mainly serve to protect the inner glass layers, which in turn play the key role in accommodating the applied load. Additionally, the outer glass layers are expected to crack to dissipate, together with the polymer interlayers, the impactor energy thus enhancing the bearing capacity of the laminated structure. Herein, the 5 LG laminate is composed of three glass layers and two PVB interlayers, whereas the 7 LG laminate consists of four glass layers bonded to three PVB interlayers. An illustrative example of such a laminate is displayed in Figure 1. Geometrical details of both composites are stored in Table 1. \begin{table}
\begin{tabular}{l l l} \hline  & **5 LG** & **7 LG** \\ \hline number of layers & 5 & 7 \\ glass type & float annealed & float annealed \\ interlayer material & PVB (TROSIFOL BG R20) & PVB (TROSIFOL BG R20) \\ number of tested samples & 4 & 4 \\ width \(b\) (mm) & 500 & 500 \\ length \(l\) (mm) & 500 & 500 \\ thicknesses of layers (mm) & 5/2.28/6/0.76/5 & 5/1.52/8/0.76/8/0.76/5 \\ \end{tabular}
\end{table} 
Table 1: Geometry of 5-layer (5 LG) and 7-layer (7 LG) laminated glass samples. Figure 1: Example of a laminated glass. The tested samples were suspended in a vertical position on a pair of steel ropes along vertical edges to approximate free boundary conditions [13], thus eliminating the effect of mechanical supports. The low velocity impact was induced horizontally via an 800 mm long pendulum device (impactor) having a cylindrical shape with a hemispherical nose with the diameter of 50 mm. The required impact energy, defined as the kinetic energy of the impactor \(E_{\text{imp}}=0.5~{}m_{\text{imp}}p_{\text{init}}^{2}\) with the impact velocity \(v_{\text{init}}=\sqrt{2 gh_{\text{imp}}}\), was achieved by dropping the 48.2 kg impactor from a given height \(h_{\text{imp}}\). To examine the influence of subsequent impacts of growing intensity on a laminate fracture response, the impact height was gradually increased by 5 cm as seen in Table 2.  
For illustration, we present the results of three particular samples of the two laminates. The response of individual samples after individual impacts is summarized in Table 2. Considering the impacted glass on the left-hand side, the empty circle \(\left|\circ\right|\) indicates the onset of damage in a given ply, whereas the filled circle \(\left|\bullet\right|\) identifies a glass layer which has already been broken during previous impacts. Empty spaces \(\left|\right|\) represent unbroken glass layers. Although limited to three samples only, the results confirm the advantage of a sacrificial-glass-ply design which expects the outer glass layers to fracture, so the inner glass layers are still capable of sustaining further loads. This is particularly evident for samples where the impacted glass layer fractured at the initial stage of loading (5 LG-1, 7 LG-1, 7 LG-3). Unfortunately, the results also suggest a certain degree of variability in fracture response of laminates potentially attributed to a random distribution of initial surface flaws of unprotected (outer) glass layers. This was also confirmed by our study on a single glass ply in [14] devoted merely to the application of various damage models implemented in the LS-DYNA software. These findings make the predictive capability of any numerical model rather difficult especially in the framework of deterministic modeling. To perform stochastic simulations goes, however, beyond the present scope owing mainly to insufficient experimental data to identify, for example, a statistical distribution of impact energies. Instead, we concentrate on tuning the computational model to represent one particular experiment. If successful, this will serve as a stepping stone for more complex stochastic analysis.