Abstract: The crack initialization life and crack propagation life of turbine disc slots at high temperature under the fatigue/creep interaction are studied according to damage mechanics.The modified Chaboche's damage model of low cycle fatigue and the improved Kachanov's damage model of the creep crack propagation have been combined to establish a nonlinear damage accumulation model.A model of crack propagation under fatigue/creep interaction has been developed,based on the above mentioned model.The good agreement between the calculated results and experimental data demonstrates that the model is quite effective.Damage FEM has been developed according to damage mechanics and FEM.The method uses finite element mesh dimension to simulate damaged crack length.The criteria for the crack initialization and the crack propagation orientation are established and testified by the calculation of the fir-tree slots of a turbine disc under the two kinds of loading conditions.The effects of mesh's minimum dimension,the stress boundary condition and the displacement boundary condition of the calculation model on the crack initial life of the structure are analyzed.It is also discussed,how the calculation model scale and the peak value of trapezoid loading spectrum affect the crack propagation life of a two-dimensional structure.