Abstract: With the crystal plastic constitutive model, the uniaxial tensile and fatigue test data were fitted to obtain the relevant parameters that meet the simulation conditions, which was realized by generating the representative volume elements of macroscopic specimens. The effect of mesh size on the simulation was analysed. The cumulative plastic slip and energy dissipation were used as indicators to predict the fatigue crack initiation life, and the influence of notch size on the fatigue crack initiation life was studied.The results show that the fatigue crack initiation life of the notched specimen obtained by the established model was within two times the error band of the fatigue crack initiation life obtained in the test, indicating the model had good prediction accuracy. When the notch size was small, the fatigue crack initiation life of the specimen significantly reduced with increasing notch size; when the notch size was larger than the critical notch size, the fatigue crack initiation life of the specimen was hardly affected by the notch size.