# The Design Value for Recycling End-of-Life Photovoltaic Panels
## 4 PV Panel Thermo-Mechanical Fatigue Analysis Using a Parametric FE Model  
In order to assess the most frequent damage/failures reported in Table 6 due to falling debris and breakage from impacts, micro-cracks and the contamination of snail traces and to increase the expected duration of the PV panel, a parametric FE numerical model was developed (Figure 12) and employed in TMF optimization analysis. The h thicknesses of the different panel layers (Figure 13) and the main overall dimensions (A, B, C, E, F, G, I, L and N) visible in Figure 14 were parameterized within the range of variation, as shown in Table 8. As a consequence of the preliminary study conducted by the authors, a layer of silicone rubber of h\({}_{\text{s}}\) thickness was predicted in the interface between the layers and the support. This thickness, as we will see, plays an important role in maintaining the adhesion between the layers, limiting the thermo-mechanical stresses and prolonging the life of the PV panel. Figure 12: Parametric FE model of silicon-based PV panels with support. Figure 13: Layer thickness parameters in the FE model. A DOE optimization on the geometric parameters was carried out by simulating TMF stress with the commercial code ANSYS Thermo-Mechanical Fatigue(r) vers 18.0. Tetrahedral ten-node elements were used to calculate the structural deformation of the layer panel with a 6000 Pa pressure (solicitation required by the standards set out in Section 3.2) acting on the top surface of the panel, and a fixed joint was used to lock the panel support on the ground (Figure 12). Static structural simulations and TMF simulations with structural and thermal cyclic loads were repeated in turn, considering all possible combinations between geometric parameters in a DOE analysis [26, 27]. The physical and mechanical parameters used in the simulations were those of Table 2. Values of silicone rubber were added to them, as shown in Table 9. The curves S-N of the materials were taken from the literature [28, 29, 30]. In the fatigue calculation, it was assumed that all the PV panel component tensions remained in the elastic field and were low enough. Two cyclic stresses were applied simultaneously to the PV panel:  
Figure 14: Overall dimensional parameters in FE model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **Value** & \multirow{2}{*}{**Opt. Value**} & \multirow{2}{*}{**Parameter**} & **Values** & \multirow{2}{*}{**Opt. Value**} & **Parameter** & **Values** & \multirow{2}{*}{**Opt. Value**} \\  & **[mm]** & & & **[mm]** & & &  
* a low-frequency mechanical load with a constant amplitude between 0 and 6000 Pa pressure (maximum mechanical load required by the standards set out in Section 3.2) (Figure 15a);
* thermal stress with a daily cyclic frequency and variable amplitude between -40 \({}^{\circ}\)C and 90 \({}^{\circ}\)C (operating temperature required by the standards set out in Section 3.2) (Figure 15b). The dimension of 0.4 \(\pm\) 0.1 for the thickness of standard PV cells (mono or polycrystalline commercial PV cells) was taken as fixed data, and the thicknesses of each of the other layers, in order to guarantee longer durability with a similar layer stress, were evaluated. Factors of safety and total life cycles by equivalent von Mises stress are shown in Figure 16a and in Figure 16b, respectively. In both TMF simulations, the PV cell layer was found to be the most critical component. However, using a proper thickness (h\({}_{\text{s}}\)) of the silicone rubber layer, it is possible to increase the safety factor by more than 40% (Figure 16c) and the total life cycle (Figure 16d) of the PV panel. The use of a silicone rubber layer also guarantees excellent impact resistance and the finest coupling and insulation conditions. In Table 7, highlighted in bold, the best values of geometric parameters that guarantee the greatest value of the total life are presented.