13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- ( )n da A K dN = • Δ （） a—Crack length,N—Cycle, KΔ —Stress intensity factor range, A, n material constants From the formula, we can see the fatigue crack growth rate has a close relationship with the stress intensity factor of the materials. Stress intensity factor can be used to characterize crack toughness of the materials that the ability of gap materials to bear loads and plastic deformation under slow loading and linear elastic properties. Generally the critical stress intensity factor ( CK ) is used to describe it. Generally speaking, the structure crack toughness, especially steel, increased with temperature, the destroyed stress intensity factor will increase the range and will increase the crack growth rate. Another factor of fatigue crack propagation is stress concentration .The influence of the geometric not continuity will increase the nominal stress value of bearing structure parts. For fatigue crack with stress concentration expansion laws can be shown as (2) formula express: ( )n eff da A K dN = • Δ （2） In the formula： A ，n——material constant, ( ) eff t K K a a σ Δ ∝ Δ , σΔ —Nominal stress range, a——Crack length, ( ) tK a ——The stress concentration factor. The strength problem of engineering structure , often need to estimation fatigue life of the dangerous parts in the structure. If knowing the material fatigue performance data, fatigue load spectrum, in principle we can estimation life by cumulative damage theory. In this article, the circulation of the cumulative damage as circulation method, namely to crack length as the measure of the damage, the initial damage is described by initial crack length, the critical damage is described by critical crack length,the cumulative damage produced by each load cycles is described wit the crack propagation incremental produced by one load cycles. So damage accumulation formula can express into (3) type: 0 0 1 1 ( ) c c N N c i i i i da a a a a dN = = = + Δ = + Δ ∑ ∑ （3） ca—Critical crack length, 0a—Initial crack length, iaΔ —Crack propagation incremental, i — Cycle time, cN — Cycle times reached the critical crack length. Through the cycle by the expression of the total circulation damage theory we can see, the fatigue life of the component has a close relationship to the crack growth rate In practical engineering, the maximum length of fatigue crack propagation general is considered to be certain value, we usually think the maximum length of bolt connection is the pure distance between two bolt hole. So the crack’s growth rate directly affects the fatigue life of components. 3 The finite element analysis 3.1 Calculation model size and material parameters
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