5. Effect of compression stress on fatigue thresholds
From the values of R and ΔK th as shown in Tables 3 and 4, the maximum stress intensity factorsK max are normalized byΔK th0, where ΔK th0 is the threshold at R = 0. Table 5 shows the ratioK max/ΔK th0 at negative stress ratio R for ferritic steels and aluminium alloys. The ratios K max/ΔK th0 are also shown in Figure 8 as a function of the stress ratio R . It can be seen that the ratioK max/ΔK th0 decreases with decreasing stress ratio R . This means that the thresholds at negative stress ratios are slightly affected by compression stresses, as suggested by ASTM E 647.
Based on the experimental data forK max/ΔK th0, the lower bound of K max/ΔK th0 can be obtained semi-empirically by a function of stress ratio R , as shown in Figure 8. The relationship betweenK max/ΔK th0 and R is expressed by
K max/ΔK th0 = (1 - 0.7R )/(1 - R ) . (6)
When R is decreasing, compression stress gradually influences the threshold value in accordance with Equation (6). For example, the thresholds decreases to 85% due to compression stress at R = -1, and to 75% due to compression stress at R = -5.
Figure 8 also illustrates the ratioK max/ΔK th0 as per the WRC Bulletin, IIW and BS 7910. The ratiosK max/ΔK th0 as per the WRC Bulletin and IIW are constant at 1.0, irrespective of materials, becauseΔK th = K max = constant at all negative ratios R . The definition of the threshold in BS 7910 is expressed by K max- K min= constant, and the K max is expressed byK max = ΔK th/(1 - R ) and ΔK th0 = constant. Then, the ratioK max/ΔK th0 as per BS 7910 is easily obtained by
K max/ΔK th0 = 1/(1 -R ) . (7)
The ratio K max/ΔK th0denoted as per BS 7910 is also irrespective of materials. The ratioK max/ΔK th0 significantly decreases with decreasing stress ratio R .
Conclusively, based on the experimental results, thresholds at negative stress ratios are affected by compression stress. The thresholds given in the WRC Bulletin and IIW are not affected by compression stress, and the thresholds given in the WRC Bulletin and IIW are slightly unconservative. The thresholds given in BS 7910 decrease rapidly with decreasing stress ratio R , and the thresholds given in BS 7910 are significantly conservative.
Using Equation (6), the threshold for each material at negative stress ratios can be expressed as follows:
K max - K min =ΔK th0 (1 - 0.7R ) (8)
When the threshold ΔK th0 is only known atR = 0, the threshold at negative stress ratios for each material can be estimated by Equation (8). For example, the threshold for SM 410 is ΔK th = 8.8 MPa √m at R = 0, as shown in Table 3. For the threshold at R < 0, Equation (8) may be written as K max - K min= 8.8(1 - 0.7R ), and the threshold at R = -1 becomesK max - K min = 14.96, which is in good agreement with 15.0 in Table 3. From the perspective of application in flaw evaluation procedures, the definition of thresholds at negative stress ratios can suitably be written using variable threshold values with K max -K min, because fatigue tests are conducted on testing machines by pre-setting the values σmax and σmin, so the tests proceed within this interval.