13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- In the above equation, i KΔ is the average SIF range of the ith step and can be defined as ( ) 1 / 2 i i i K K K − Δ = Δ +Δ , (8) where ΔKi-1 and ΔKi are the amplitudes of SIF corresponding to ai-1 and ai, respectively, and can be determined using the SFBEM presented in section 2. The procedure for fatigue life prediction based on SFBEM is as follows: 1. Determine the initial SIF range ΔK0 corresponding to the given initial crack size a0 using the SFBEM in conjunction with the Erdogan fundamental solutions. 2. Check if ΔK0>ΔKth. If yes, the propagation of the crack will occur. 3. Assume the crack growth size of the ith step to be Δai=ηai-1 (i=1,2,…), in which η=0.1~0.01. Then the crack size of the ith step is 0 1 i i j j a a a = = + Δ∑ . 4. Determine the SIF range ΔKi corresponding to ai using SFBEM. 5. Calculate the average SIF range of the ith step i KΔ using Eq. (8). 6. Calculate the number of cycles of the alternating stress of the ith step ΔNi using Eqs. (6) and (7). 7. Check if Ki(σmax)<KIc. If yes, go to step 3. If no, then stop. Assume the final step number is n. Then the fatigue life can be obtained as p 1 n i i N N = = Δ∑ . (9) 4. Numerical examples 640mm 640mm 2a Δ σ Δ σ Figure 3. A square plate with a center crack Fig.3 shows a square plate with a center crack subjected to a cyclic loading with Δσ=200MPa (σmax=200MPa, σmin=0). The fatigue threshold and the fracture toughness of the material are taken to
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