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.