13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- 3. Fatigue life and fatigue damage analysis 3.1. Fatigue life test At room temperature and atmospheric pressure, the fatigue tests for smooth samples of GH4133B superalloy are performed on a servo hydraulic test machine (CSS-280S-20) of ±20kN loading capacity. Under symmetrical cyclic loading condition (30 Hz sine wave, stress ratio R=−1), the fatigue life tests are carried out at various stress amplitudes. The fatigue limit is defined as 107 cycles. The stress amplitudes are assigned as 256MPa, 320MPa, 400MPa, 432MPa, 462MPa and 538MPa, respectively. In the case of stress amplitude as 256MPa or 538MPa, only one fatigue test for a smooth sample is carried out, while for the other stress amplitudes, four fatigue tests are performed for eight smooth samples of GH4133B superalloy. During the process of fatigue tests, a multi-parameter measurement mode is adopted, that is, except for recording the number of fatigue loading cycles, the values of electric resistance of smooth sample are measured every certain number of loading cycles by a QJ-57 type DC resistance bridge whose scale overs the range from 0.01μΩ to 1.1111kΩ, which is producted by Shanghai Sute Electrical Appliance Limited Company. Therefore, the accumulated fatigue damage for the sample of GH4133B superalloy during the fatigue process is monitored by measuring electric resistance change. 3.2. Fatigue life analysis Using the up-down stress amplitude method, the fatigue life measured in the tests is determined as 288MPa, which is the mean value of stress amplitude 256MPa and 320MPa. The three-parameter power function expression is adopted to describe the fatigue S-N curve, that is m N − − = ) ( ac f a f σ σ σ , (1) where, Nf is fatigue life, σf, σa and m are undetermined coefficients, and σac is theoretical fatigue limit. Usually, the value m is obtained as 2 to 4. In this work, the value m is set as 2. Taking logarithm on both sides of above equation, and the equation can be rewritten as ) 2lg( lg lg ac a f f σ σ σ − = − N , (2) Eq. (2) shows a linear relationship between logarithmic fatigue life lgNf and lg( σa− σac), and the slope is 2. According to the experimental data obtained from the fatigue life tests, using a standard normal distribution function to calculate the values of fatigue life at survival probabilities as 50%, 90%, 95% at various stress amplitudes, the P-S-N equations at survival probabilities as 50%, 90% and 95% are individually achieved by using nonlinear regression method as 2 a 10 f ) 2.987 10 ( 233.43389 − − = × σ N , (3) 2 a 10 f ) 2.008 10 ( 229.50659 − − = × σ N , (4) 2 a 10 f ) 1.795 10 ( 228.36174 − − = × σ N , (5) It can be seen that the theoretical fatigue limit σac in Eq. (1) is calculated as 233.43389MPa, and the experimental one is measured as 288MPa, the relative error is about 18.95%. According to Eq. (3), Eq. (4) and Eq. (5), the P-S-N curves at survival probabilities as 50%, 90% and 95% are individually plotted, and are compared with the estimated values of fatigue life, as shown in Fig. 3. It can be found from Fig. 3 that the theoretical P-S-N curve is well fitted with the estimated values of fatigue life at survival probability as 50%, while at survival probabilities as 90% and 95%, there are some difference between the theoretical curves and the estimated values. 3.3. Fatigue damage analysis As aforementioned above, during the process of fatigue life tests, the multi-parameter measurement
RkJQdWJsaXNoZXIy MjM0NDE=