13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- ( ) ( ) th d d m a C K K K N = Δ Δ >Δ , (4) where a is the crack size; N is the number of cycles of the alternating stress; ΔK=K(σmax)-K(σmin) is the SIF range; ΔKth is the fatigue threshold, which means if ΔK≤ΔKth, the crack is assumed to be non-propagating; C and m are the material constants obtained from experiments. By integrating Eq. (4), the crack growth-based fatigue life can be obtained as ( ) c 0 p d a m a a N C K = Δ ∫ , (5) where a0 is the initial crack size; ac is the critical crack size at fatigue failure and can be determined using the fracture toughness KIc. Generally, the explicit solutions to SIFs for most engineering problems are not available. Therefore, numerical approaches are required for fatigue life prediction when using Eq. (5). 3.2. Fatigue life prediction using SFBEM a0 Δa1 a1 a2 ai-1 ai an-1 an Δa2 Δai Δan (ac) ΔN1 ΔN2 ΔNi ΔNn Δσ ΔK1 ΔK2 ΔKi ΔKn ΔKi-1 ΔKn-1 ΔK0 ... ... ... ... ... ... ... ... ... ... ... Δσ Figure 2. Propagation of a crack The propagation of a crack from the initial crack size a0 to the critical crack size ac can be illustrated in Fig.2. The number of cycles of the alternating stress corresponding to the ith step of the crack growth can be approximately expressed as d d i i i a N a N Δ Δ = ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ , (6) where Δai is the crack growth size of the ith step; d d i a N ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ is the average crack growth rate during the current step and can be determined using the Paris equation, that is ( ) d d m i i a C K N ⎛ ⎞ ⎜ ⎟ = Δ ⎝ ⎠ . (7)
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