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The propagation form of the preset edge crack in The nano Single crystal gamma-TiAl under different strain rate were simulated by the method of molecular dynamics in this paper, velocity loading way was used to obtain dynamic uniaxial tensile for preset edge crack in the single crystal gamma-TiAl within 5.0*10₇S_-1~7.5*10₉ S_-1. The results showed that the crack propagation form varies with the range of strain rate. In the non-sensitive region(≤4*10₈ S_-1), the crack propagates in a brittle cleavage manner. In the sensitive region(4.0*10₈ S_-1＜the strain≤1.0*10₉ S_-1), it was cleavage extension features Early,the slip dislocation was emitted from the crack tip, and the void defect initiates the place where dislocation piled up and then growed to the child crack later,the child crack linked the main crack when it biased 45-degree under the strain≤5.0*108 S_-1,but it connected the main crack at the same direction under 5.0*10₈ S_-1＜the strain≤1.0*10₉ S_-1,thus leaded to the fracture both finally； In the sharp-change region(≥1.0*10₉ S_-1), the crack didn_、t craze in the maximum stress for the reinforcement of strain,and the Stress decreased for it continues to increase some time. The non-crystallizing of the atom structure occurs near the crack tip because of high strain rate, and then the micro crack initiates in area of structure disordered, the micro crack growth leads to the “test specimen” fracture eventually.