以金属的疲劳扩展区和瞬断区为对象 ,讨论了应力变化幅度与裂纹临界长度、疲劳寿命和临界裂纹长度的数学模型 ;分析了疲劳瞬断区上放射线的物理数学模型 ,探讨了疲劳瞬断的性质和控制参量以及疲劳瞬断区的对称性 ,得到了一些颇有启发性的结果 ,为金属材料的疲劳宏观断口定量分析提供了有价值的思路 Taking the fatigue extension zone and the instantaneous zone of metal as examples, the mathematical models of the stress variation range, the critical length of the crack, the fatigue life and the critical crack length are discussed. The physical mathematical model of the radiation on the fatigue instantaneous zone is analyzed, The nature and the control parameters of breakage and the symmetry of the fatigue snap-off region, some enlightening results have been obtained, which provide valuable ideas for the quantitative analysis of the fatigue macro fracture of metallic materials