13th International Conference on Fracture June 16–21, 2013, Beijing, China —2— Damage mechanics is a subject studying evolution law of damage field of the deformable solid, including damage and its effect on mechanical properties of materials under action of outside factors such as load, changing temperature and corrosion and so on. Based on damage mechanics theory, a relation was deduced in literature [8] as follows: S S A A Δ = Δ (1) where △A and △S were after damaged area, stress amplitude , accordingly. Constant strain is admitted as control parameter generally, so low cycle fatigue is also called strain fatigue. Under cyclic action of constant strain, grains in material may come into microcracks because of repeated slips, which will damage the material. Simultaneously, effective area of the material will decrease gradually and capacity enduring the load may drop and nominal stress acted on the material will attenuate step by step. Supposing a crack or several cracks initiated, and damage effect produced by several cracks initiated in the same section or different sections is equivalent to one crack, then attenuation of the stress and the length of the crack should meet a certain mathematical relation. When cracks don’t initiate, stress will keep constant; and cracks initiated and propagated to fracture the material, stress would drop to zero. That’s to say, ratio of reduction of the specimen area perpendicular to the direction of the crack propagation to original specimen area should be equal to ratio of attenuation of the current stress to steady stress, that is Eq. (1). Reduction of the specimen area and length of the crack propagation should satisfy some mathematic relation, which would provide a basis of damage mechanics theory for setting up the expression of a equivalent value of crack initiation to stress attenuation. Attenuation of stress can be measured by a test, and the equivalent value of crack initiation be also obtained through the built expression, and corresponding cycle is called crack initiation life. Literatures [9,10 ] indicated that several cracks initiated in the course of low cycle fatigue. It could be seen that several cracks sometimes initiated in the same section perpendicular to loading orientation, sometimes not from many tests. No matter one crack or several cracks initiated in the same section or not, damage effect should be deemed as that of one crack in one section. Figure 1 reveals above analysis. Parameters a, b and c are crack lengths located in one section or different sections, and parameters A, B and C are corresponding areas swept by above three cracks, see figure 1(1) for details. Damage effect produced by above three cracks or more equals to that by one crack d, with a corresponding swept area △AD, see figure1(2). Figure1(3) shows the geometry relations of equivalent crack length d, its swept area △AD and specimen radius r, and also is calculation model to predict crack initiation. (1) (2) (3) (1) Several cracks and corresponding swept areas (2) Equivalent to one crack and an area (3) Sketch of calculation model a B b A C c d △AD θ r o △AD d
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