In this study, a model of an axisymmetric cyclotron was established, taking the engine combustion chamber as an example. The fracture behavior of ceramic matrix composites under thermal shock conditions was systematically studied through transient heat conduction and thermodynamic coupling analysis methods. Through using the interaction integration method, a thermal stress intensity factor calculation model was established, effectively solving the limitation of the traditional J-integration method in separating mixed stress intensity factors in non-uniform materials. This study combined the finite element method to verify the effectiveness of interaction integration in the cylindrical model. The results are in good agreement with the analytical results. This article analyzed typical examples of fracture problems in ceramic-based cylindrical structures under thermal shock. The results indicate that in the early stage of thermal shock, the distribution of thermal stress shows the most significant changes, and the stress intensity factor quickly reaches its peak, then it tends to a steady-state value. Thermal shock may lead to more severe failures than stable thermal loads.