## 6 Finite Element Simulations
### Simulation of and Actual Temperatures in a Cast Polymer Block  
In Section 7.7 the actual total heat of each experiment was used to make the heat flow predictions and the experiments more comparable. For the finite element simulations however, the mean value of \(67\,\mathrm{J/g}\) was utilized. As described in Section 6 we did first a finite element simulation of the material in the bucket after mixing the components. In Figure 11 the results for one step can be seen. The time step of the shown finite element simulation is \(17\,\mathrm{min}\) and \(33\,\mathrm{s}\) since this was the moment when the core of the simulated cylinder reached the value of the very first temperature measurement (ca. 314 K). At this point the degree of cure of the core (Figure 11b) was ca. 23%. This value was used as the input parameter for the simulation of the curing process in the actual mold which contained the temperature sensors (cf. Section 5.3 and Figure 3). One step of these simulations can be seen in Figure 12.  
Since the conversion can not be measured directly, in-situ, in a large body the temperature development has to act as a proxy for information about the ongoing curing progress. In Figure 13 the measured and simulated values of sensors 11 to 15 are shown. Figure 11: Cut through the cylindrical body of the finite element simulation of the mixed material in a bucket prior the control experiment. (**a**) Temperature distribution throughout the simulated body. (**b**) Conversion of the simulated material. The time information is valid for both images. The presented measurement values and simulation curves in Figure 13 are representative for the experiment/simulation. The data of all temperature sensors is presented in Appendix F.  
Taking into account the uncertainties about the material and that mean values from the above described investigations were used, it can be stated that the measured and simulated temperature values agree well with each other. The most interesting period during the cure, for engineers to identify hot-spots in the material, is the period when the temperature is rising and when it reaches its highest value. The simulation predicts the peak temperatures within an error of max. 3 K. In addition the (time wise) peak positions and the differences for sensors at different positions are predicted very well. The simulated body cools slightly faster than the actual material in the experiment, but the overall dynamic of the temperature development is predicted correctly over three orders of magnitude in time. One minor disagreement can be seen between the simulated temperature and the actual measured temperature. From a purely physical point of view, the material closer to the edges of the block (e.g., sensors S11 and S15) should exhibit the temperature peak earlier than the material in the middle of  
Figure 12: Cut through the finite element simulation of the control experiment to simulate the curing of the material. The cut goes parallel to the y-plane along the position of the temperature sensors 11–15 (cf. Figure 3). (**a**) Simulated temperature distribution. (**b**) Conversion of the simulated material. The blue points mark the position of temperature probes 11 to 15. Figure 13: Measured (points) and simulated (lines) temperatures for a \(20\times 20\times 6\) cm\({}^{3}\)-block of material at the positions of temperature sensors 11 to 15 (cf. Figures 3 and 12). the block; simply due to the closeness to the colder outside. The underlying physical model of the finite element heat transfer simulation predicts this correct. However, we observe a slight difference between the peak positions of the measured and predicted temperature values. For the measured values the shape of the temperature curves seems to follow the core temperature, and the temperature peak occurs for all positions at the same time. We have to admit that we do not have an explanation for this behaviour. However, it has also been observed in a different kind of thermosetting polymer [83].