13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- amplitude Based on theory of fracture mechanics, K Y a σ π Δ = Δ , (2) Y-coefficient of crack shape (generally it is 1 ), σΔ -alternative stress amplitude We make (2) type substitute (1) type, we can get ( ) ( ) 0 0 1 1 c c a a m m a a da da N C K C a σ π = = Δ Δ ∫ ∫ , (2-1) Integrating, we can get ( )( ) ( ) 1 2 1 2 0 2 0 2 2 1 2 ln ln 2 m m c m m c a a m C m N a a m C π σ π σ − − ⎧ − ≠ ⎪ − Δ ⎪ = ⎨ ⎪ − = ⎪ Δ ⎩ , (1) Implied by some statistical data, initial crack length 0a of welded structure is about 0.1~1.0mm. On average, we can think that 0a is equal to 0.5mm[6]. Critical crack size ca depends on the fracture toughness and stress level of material. According to the theory of fracture, we can get: 2 1 c c K a π σ ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ , (2) Among it, cK -the fracture toughness of material, we can get it from material data; σ-structure stress Because of some uncertain factors, such as fabrication technology, material properties and environment for use, we cannot get a most realistic number of C, so there are different numbers of C in different documents. For this reason that C is a variable quantity with fuzzifrfication, we can select some point among C’s feasible region and on its edge. Then we put them into formula (3) and get their fatigue life respectively. Finally, based on the method of fuzzy comprehensive evaluation, we can make a forecast of its fatigue life. 3. Model of fuzzy comprehensive evaluation 3.1 Degree of membership Assuming 1 2 ( , , , )m C c c c = L which is the factor set that affect structure’s fatigue life, 1 2 ( , , , )n V v v v = L which is the set of evolution level. Among them, ( 1,2, , ) ic i m = L means number i influencing factors, ( 1,2, , ) j v j n = L means evolution level. So the array of degree of membership of set V is:
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