In Japan, new developments of liquid rocket engines are now underway for Japan's next flagship launch system. In the development, front-loading design process is applied to reduce development costs and to increase reliability. Therefore it is indispensable to precisely evaluate life time of a combustion chamber, which is exposed to the most severe heat and loads among engine components, in an early design phase. In order to improve accuracy in the life prediction, we focus on the interaction between thermo-fluid behaviors and structural responses, and have been developing the multi-physics coupled simulation. By applying this simulation and the linear damage rule, we have clarified the mechanisms and the dominant factors of cracks occurred in the throat, which were experienced under development of the upper stage engine. It has been revealed that the damage is caused by creep and low cycle fatigue and depends on structural temperature histories. Structural temperature overshoots in the start-up process are affected by the transient flows of both combustion gas and coolant. Due to overshooting temperature, creep and low cycle fatigue damage are accumulated.