Dependence of thermal stress evolution on power allocation during Kyropoulos sapphire cooling process

In this paper, numerical simulation has been carried out to study effect of heater power allocation on the thermal stress evolution during Kyropoulos sapphire cooling process. Characteristics of the temperature and stress distributions during the whole cooling process are firstly analyzed. A design of divided side heater is then proposed for a flexible power adjustment. The transient profiles of thermal stresses are obtained from analysis of the typical power allocation ratios of the top part to the lower part of the side heater. The results show that during the cooling process large stresses usually present in the regions near the 'throat' and 'bottleneck' of the crystal. The highest stress turns up at the bottleneck during the naturally cooling process occurred after the power is off. The results further indicate that the von Mises stress significantly decreases as the power radio increases. Additionally, the maximum stresses for a higher power ratio under the range of the current study are always smaller than that of a lower one before reaching the peak values, which is beneficial to avoid thermal stress-related defects. Based on the analysis, optimized power allocation of the side heater is recommended.