Dynamics and generation of stress waves in cracked graphite moderator bricks

Abstract

In the present study, static and dynamic analyses have been performed for graphite moderator bricks with and without key grooves under the different initial loading conditions of pure bending and slot rotation by using the finite element method. The possibilities of the occurrence of multiple cracking due to internal stresses have been investigated in terms of the (1) initial loading condition; (2) vibration mode shapes; and (3) damping of the bricks. Firstly, modal dynamic analysis has been carried out, and the effect of the initial loading conditions, such as pure bending and slot rotation, on the dynamic stress responses was investigated. It was found that stress enhancement was more significant under the condition of pure bending than that of slot rotation. For pure bending, the key groove which was opposite to the primary cracking site had the maximum dynamic circumferential stress. This implied that secondary cracking might occur at this position under pure bending. Secondly, in order to investigate the dominant mode shape for the stress enhancement, natural frequency analysis has been conducted. Fast Fourier Transformation (FFT) has also been performed to convert time–domain stress responses into frequency–domain stress responses. The initial loading conditions determined which mode shape was dominant for the stress enhancement. It was also suggested that a fundamental mode shape principally contributed to the occurrence of the multiple cracking. Thirdly, modal damping analysis has been performed, and the effect of damping on the stress enhancement was studied. It was found that damping had little effect on the initial peak of the dynamic stress response. This suggested that secondary cracking might still occur at the key groove opposite the primary cracking site, even if damping was present. The results of the analysis give a fundamental insight into the mechanism that may lead to multiple cracking in graphite components subject to internal stresses. However, the effects of 3-D, crack propagation speed and external restraint have not been taken into consideration in the present study. These effects may mitigate the possibility of secondary cracking, and are parts of further investigation.