13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- mode is applied to measure the electric resistance of GH4133B superalloy samples every certain numerber of loading cycles at various stress amplitudes. According to the definition of damage variable, the damage variable D charaterized by electric resistance can be written as R R D 0 1= − , or R R R D +Δ Δ = 0 , (6) where, R0 is the electric resistance before damage, R is the electric resistance after damage, and ΔR is the difference between R and R0, which is called as electric resistance change. In this work, a modified Chaboche damage model is derived to describe the damage evolution, that is 1/(1 ( ) ) f 1 a 1 1 β σ β + + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = − − N N D , (7) Substituting Eq. (6) into Eq. (7), the fatigue damage evolution equation characterized by electric resistance change can be written as 1 1 1/(1 ( ) f 0 1 a − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = − Δ + − + β σ β N N R R , (8) where, N is the number of fatigue loading cycles, Nf is the fatigue life, β and β1 are the fatigue parameters, and the parameter β1 is the function of the stress amplitude σa. 106 107 250 300 350 400 450 500 P=50% P=90% P=95% 90% 95% Stress amplitude σa Fatigue loading cycles Nf 50% Figure 3. P-S-N curves at different survival probabilities According to Eq. (8), the theoretical damage evolution equations at various stress amplitudes are derived using the nonlinear regression analysis of experiment data obtained in the electric resistance tests. Corresponding to stress amplitudes applied as 320MPa, 400MPa, 432MPa and 462MPa, the values of damage parameter 1+ β+ β1( σa) are determined as 26.543, 31.571, 40.177 and 46.822, respectively. The comparisons between theoretical fatigue damage evolution curves and test data are shown in Fig. 4. Corresponding to the various stress amplitudes, the accumulated fatigue damages of two samples in each group are collected. In Fig. 4, the square symbols denote the test date obtained from the first sample, while the circle symbols denote the test data obtained from the second sample of each group, and the solid lines represent the theoretical results. It can be found from Fig. 4 that the theoretical predicted values are in good agreement with the experimental data, which indicates that the electric resistance change ratio under cyclic loading can be used to describe the process of fatigue damage evolution of GH4133B superalloy. In the fatigue nucleation and small crack propagation stage (stage I), the fatigue damage is mainly dominated by a process of microdamge nucleation. Furthermore, due to the tension-pressure mode of cyclic loading, the action of compressive stress results in some small crack interfaces colsed, leading to the corresponding electric resistance change smaller, which can be reflected from Fig. 4(a) to (d), that is, the damage increases slowly with number of cycle in the early part of damage evolution curve. With the propagation and coalescence of small cracks, the damage degree becomes
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