# Thermal Failure Propagation in Lithium-Ion Battery Modules with Various Shapes
## 3 Results and Discussion
### Discussion  
The times to each phase of failure for modules with various shapes (triangle, rectangle, parallelogram, line, hexagon, and square) are summarized in Figure 23, where (1) and (2) represents the module with and without discharging treatment, respectively. As can be seen, most of the times to the first phase of failure floated around 400 s. Among them, the hexagon module without discharging treatment had the largest value of time to failure. It implied that failure propagated to the batteries in the first phase of hexagon modules took the longest time. It may be explained by the larger number of batteries in the first phase of hexagon modules, which delayed the propagation. As for the second phase of failure, most of them floated in the range of 500-650 s. Obviously, it was much faster when failure propagated from the first phase to the second phase than between the heater and the first  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **With Discharging Treatment** & **Time to the First Phase (s)** & **Time to the Second Phase (s)** & **Time to the Third Phase (s)** & **Propagation Speed (mm/s)** & **Mass Loss (g)** \\ \hline
1 & Yes & 391 & 612 & 735 & 0.069 & 84.0 \\
2 & No & 412 & 636 & 863 & 0.059 & 83.0 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The detailed information of square modules in tests.  
Figure 21: The domino effect of thermal failure propagation in square module.  
Figure 22: The typical curves of mass loss for square modules in tests.  
phase. It was caused by the larger amount of heat from the failed batteries. According to the results of previous experiments [29], a single 18650 battery had an average heat-output power of 600 W during the thermal runaway process which was relatively higher than that of the heater. In the second phase of failure, the propagation exhibited the slowest speed in the linear module without discharging treatment. It was due to the relatively smaller contact area in the linear module which restricted the failure propagation. It even lagged behind the third phase of failure in the rectangle module and parallelogram module. Finally, only the rectangle module, parallelogram module, and square module had the third phase and it took a longer time when thermal failure propagated to the outermost phase of battery in the square module. It resulted from the longer propagation distance in the square module, 50.9 mm compared to that of the others, 36 mm and 46.8 mm.  
In addition, the propagation speeds of the modules described above are plotted in Figure 24, where the numbering 1, 2, 3, 4, 5, and 6 represents the triangle module, rectangle module, parallelogram module, line module, hexagon module, and square module, respectively. It could be found that the failure propagation in the parallelogram module was the worst due to the largest propagation speed it exhibited. Conversely, the triangular module and the linear module presented much better safety, as their propagation speeds were smaller than the others. After combining with the space utilization as displayed in Figure 25, the triangular module may be the best choice of battery module with a lower failure propagation hazard and a higher space utilization.  
Finally, for the real battery packs or modules with BMS/cooling systems, the thermal failure propagation would not be so severe and it could be restricted somewhat under the effect of the system. Compared to the simplified modules, the discharging treatment would be suspended earlier by the BMS once the temperature of the module increased above the threshold. Nevertheless, the propagation characteristics might be homologous after the failure of the BMS/cooling system and the domino phenomenon also existed. In summary, the information in this paper may be of interest from a safety design perspective and the related work in the real battery modules shall be conducted to meet the practice in the future.  
Figure 23: Time to each phase of failure for modules with various shapes.