# Thermal Failure Propagation in Lithium-Ion Battery Modules with Various Shapes
## 3 Results and Discussion
### Linear Module  
Figure 13 shows the surface temperature curves of batteries in linear modules. Different from the results above, only the two batteries close to the heater took thermal failure during tests. This was due to the smaller contact area between batteries in the linear module and the longer distance from the heater. Different from the other modules, there was only one battery in each phase of the linear module which restricted the heat propagation. As revealed in Figure 14, the two batteries near the heater were destroyed severely and their plastic shells had been entirely burned away. It was the result of thermal failure which caused the violent ejection and combustion. As for the battery in the middle, its breakage was not as serious as the two batteries above, which was because the battery only had gases releasing instead of thermal runaway. The heat propagated to it was not enough to support its thermal runaway, although it could be observed that there were some electrolyte residuals in the positive pole which were ejected from the battery. From Figure 13, it is revealed that the two phases of thermal failure in the linear module with discharging treatment took place at 372 s and 681 s, respectively. As for the module without discharging treatment, the times were 385 s and 777 s, respectively. For both of them, the surface temperature of the battery in the middle rose obviously after the thermal runaway of the second battery and it stabilized at approximately 180 \({}^{\circ}\)C. Not only the heat propagated to it, but also the heat generated inside the battery were insufficient to increase the temperature further. Therefore, the battery stayed at the thermal equilibrium. After observing for 250 s, the heater was turned off and the battery temperature declined subsequently. Regarding the remaining two batteries, their temperatures did not have huge change. In linear modules, thermal failure propagated furthest to the second battery with a propagation distance of 36 mm, which is further listed in Figure 15. Therefore, the propagation speed was 0.053 mm/s and 0.046 mm/s, corresponding to the two modules, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **With Discharging** & **Time to the** & **Time to the** & **Time to the** & **Propagation** & **Mass Loss (g)** \\  & **Treatment** & **First Phase (s)** & **Second Phase (s)** & **Third Phase (s)** & **Speed (mm/s)** & **Mass Loss (g)** \\ \hline \(1\) & Yes & 377 & 533 & 626 & 0.075 & 51.9 \\ \(2\) & No & 399 & 554 & 651 & 0.072 & 49.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The detailed information of parallelogram modules. Figure 12: The typical curves of mass loss for parallelogram modules. respectively. Obviously, the thermal failure propagation in the linear module was relatively slower than in the other shapes, especially for the linear module without discharging treatment. Besides, the typical curves of mass loss for linear modules in tests are presented in Figure 16. Compared to the others, the linear modules exhibited much slighter mass losses of 26.0 g and 22.3 g, corresponding to the two linear modules with and without discharging treatment, respectively. The specifics are listed in Table 5.  
Figure 13: The typical surface temperature curves of batteries in linear modules: (**a**) with discharging treatment; (**b**) without discharging treatment. Figure 16: The typical curves of mass loss for linear modules in tests. Figure 14: The photograph of linear module after test. Figure 15: The domino effect of thermal failure propagation in linear module. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **With Discharging** & **Time to the First** & **Time to the** & **Propagation** & \multirow{2}{*}{**Mass Loss (g)**} \\  & **Treatment** & **Phase (s)** & **Second Phase (s)** & **Speed (mm/s)** & \\ \hline
1 & Yes & 372 & 681 & 0.053 & 26.0 \\
2 & No & 385 & 777 & 0.046 & 22.3 \\ \hline \hline \end{tabular}
\end{table}