13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- for each group. The approach of specified number of fatigue loading cycles is applied to determine the threshold stress intensity factor range ΔKth, and an EVO scanning electron microscope is applied to investigate the fracture surface morphologies of samples of GH4133B superalloy. 4.2. Fatigue crack propagation behavior As the stress ratio R=0.02, 0.1, 0.2 and 0.4, the threshold stress intensity factor ranges ΔKth measured in the tests are 11.842MPa·m1/2, 11.313MPa·m1/2, 9.773MPa·m1/2 and 7.440MPa·m1/2, respectively. The relationship between the crack propagation rate da/dN and stress intensity factor range ΔK is shown in Fig. 5(a). It can be found from Fig. 5(a) that the crack propagation rate da/dN increases with increasing stress intensity factor range ΔK, and with increasing stress ratio. However, under the condition of low stress intensity factor ranges, the differences among the experimental data of crack propagation rate at different stress ratios are very small, which indicates that the effect of stress ratio on fatigue crack propagation rate are weak at low stress intensity factor ranges. The Paris formula is applied to carry out a regression analysis for experimental data of fatigue crack propagation at various stress ratios. The Paris formula is written as m C K N a ( ) d d = Δ , (9) where, a is crack length, N is number of fatigue loading cycles, C and m are parameters determined by the crack propagation tests. Taking logarithm both sides of Eq. (9), Eq. (9) can be rewritten as ) lg( lg d d lg C m K N a ⎟ = + Δ ⎠ ⎞ ⎜ ⎝ ⎛ , (10) It can be seen from Eq. (10) that the relationship between crack propagation rate da/dN and stress intensity factor range ΔK shows a linear one in double-logrithmic coordinates, and the slope and intercept are individually m and lgC. At stress ratio R=0.02, 0.1, 0.2 and 0.4, the experimental data of fatigue crack propagation are analyzed by Eq. (10) using the least square regression method, and the crack propagation rate equations are individually derived as ) lg( 8.229 2.700 d d lg K N a ⎟ =− + × Δ ⎠ ⎞ ⎜ ⎝ ⎛ , (11) ) lg( 8.403 2.858 d d lg K N a ⎟ =− + × Δ ⎠ ⎞ ⎜ ⎝ ⎛ , (12) ) lg( 8.807 3.171 d d lg K N a ⎟ =− + × Δ ⎠ ⎞ ⎜ ⎝ ⎛ , (13) ) lg( 8.587 3.176 d d lg K N a ⎟ =− + × Δ ⎠ ⎞ ⎜ ⎝ ⎛ , (14) According to Eq. (11), Eq. (12), Eq. (13) and Eq. (14), the theoretical curves of crack propagation rate versus stress intensity factor range are plotted, as shown the solid lines in Fig. 5(a). It can be found from Fig. 5(a) that the theoretical results are in good agreement with the experimental data, and the value of slope m increases monotonously from 2.700 to 3.176 with increasing stress ratio from 0.02 to 0.4, indicating that the crack propagation rate increases with increasing stress ratio, which is consistent with the aforementioned experiment results. Therefore, the Paris formula can be used to describe the fatigue crack propagation behavior of GH4133B superalloy. Intending to describe the crack propagation behavior in the fatigue tests of GH4133B superalloy at any stress ratio more precisely, a threshold stress intensity factor range ΔKth is introduced into Eq. (9), and the Paris formula is modified as n B K K N a ) ( d d th = Δ −Δ , (15)
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