13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- be ΔKth=5.5MPa·m1/2 and KIc=104MPa·m1/2, respectively. The material constants C and m in the Paris equation are assumed to be C=6.9×10-12 m/cycle/(MPa·m1/2)3 and m=3, respectively. The initial crack size is taken to be a0=0.5mm. 4.1. Analytic solution Since the crack size is much smaller than the size of the plate, the SIF in this case can be approximately determined using the analytic solution for an infinite plate with a crack, that is K a σ π = . (10) It can be deduced from the above equation that 1 1 2 2 0 0 th 7.927MPa m 5.5MPa m K a K σ π Δ =Δ = ⋅ >Δ = ⋅ , (11) and thus the crack propagation will occur. From Eq. (10), we also have 2 Ic c max 1 86.07mm K a π σ ⎛ ⎞ = = ⎜ ⎟ ⎝ ⎠ . (12) Therefore, the fatigue life can be obtained using Eq. (5) as follows: ( ) ( )( ) c 0 5 2 1 2 1 0 c d 1 1 1 2.688 10 cycle 2 1 a m m m m a a N a a C K C m σ π − − ⎛ ⎞ = = − = × ⎜ ⎟ Δ ⎝ ⎠ − Δ ∫ . (13) 4.2. Numerical solution When using SFBEM to calculate the SIF of the plate, 16 fictitious boundary elements and 40 boundary segments are adopted, and the distance between the fictitious boundary and the real boundary is taken to be d=40mm. The value of the coefficient η in step 3 of section 3.2 is assumed to be 0.1. In the calculation, 53 steps of crack propagation have been involved in total. The results obtained by the present method are listed in Table 1. For the purpose of comparison, the results of the analytic solution are also presented in the table. Table 1. Results of fatigue life prediction Method ΔK0 (MPa·m1/2) a c (mm) Np (cycle) Present method 7.928 74.57 2.652×105 Analytic method 7.927 86.07 2.688×105 It can be seen from Table 1 that, for the fatigue life of the plate, the results obtained by both methods are in good agreement, while for the critical crack size, certain discrepancy occurs. Actually, as the crack size increases with propagation, the error of Eq. (10) corresponding to the case of infinite plate becomes larger, leading to the error of the critical crack size in the analytic solution, as shown in Fig.4. But as the crack size approaches the critical size, the number of cycles at this stage contributes much less to the fatigue life. Therefore, good agreement is still observed for the prediction of the fatigue life between the two methods, as can be seen from Fig.5.
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