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Adopt two types of damage variables,  and , and make the bidirectional combined coordinate system and the bidirectional curves in the whole process, describing their damage evolutive behaviors on fatigue damage-fracture to elastic-plastic steels; communicate the cross-referencing between their computing models and between describing curves at each stage among varied disciplines; bring forward a viewpoint about the driving force of material damage, that is the damage stress factor at crack forming stage, Provide the computation expressions and computing methods of the strength problem of materials with short crack and long crack at each stage; reveal the geometrical and the physical meaning of force triangle and its edge vector at each stage, Provide the conversion methods between the variables, the equations, the material constants and the dimensional units; Indicate the physical and the geometrical meanings for some key parameters. This will be having practical significance for promoting developing, and applying each discipline.

The Computing of Intersectant Relations for Its Strength Problem on Damage and Fracture to Materials with Short and Long Crack