3.1 Fatigue thresholds given in flaw evaluation documents
WRC (Welding Research Council) Bulletin 194 gives thresholds for mild,
low-alloy and austenitic steels as follows [5]:
ΔK th = 6.4(1 - 0.85R ) ksi√in. = 7.0(1 -
0.85R ) MPa√m for 0.1< R <1.0, and
ΔK th = 5.5 ksi√in. = 6.0 MPa√m for R ≤
0.1.
Figure 1 illustrates the relationship betweenΔK th and the stress ratio R for steels.
The threshold ΔK th increases with decreasing
stress ratio R . When R < 0.1,ΔK th is given by a constant value. The definition
of ΔK th for R < 0 is not clearly
stated. It appears that the threshold at negative stress ratios is
expressed by K max only.
The International Institute of Welding (IIW) Commission gives thresholdsΔK th in units of MPa√m for ferritic steels at
elevated temperature and for aluminium alloys [6]. TheΔK th for ferritic steels is given as follows:
ΔK th = 2 for 0.5 ≤ R ,
ΔK th = 5.38 - 6.77R for 0 ≤ R< 0.5, and (3)
ΔK th = 5.38 for R < 0.
The relationship between ΔK th and the stress
ratio R for ferritic steels is shown in Figure 1. The thresholdΔK th for ferritic steels is a constant value forR < 0.
The ΔK th in units of MPa√m for aluminium alloys
given by IIW is as follows:
ΔK th = 0.7 for 0.5 ≤ R ,
ΔK th = 1.8-2.3R for 0 ≤ R< 0.5, and (4)
ΔK th = 1.8 for R < 0.
The threshold ΔK th for aluminium alloys is also a
constant value for R < 0. Figure 2 depicts the
threshold for aluminium alloys. The definition of the threshold forR < 0 is not given in the IIW Commission document. The
definition of the threshold for R < 0 for steels and
aluminium alloys is deemed to be K max only.
British Standards (BS) 7910 gives recommended fatigue crack growth
thresholds for steels (excluding austenitic steels) and aluminium alloys
for assessing welded joints and unwelded components [7]. For
unwelded steels (excluding austenitic steels) in air and with cathodic
protection in marine environments at temperatures up to 20oC, the thresholds ΔK th given
by BS 7910 are the same as in Equation (3).
For welded joint aluminium alloys, the threshold in air or
non-aggressive environments at temperatures up to 20oC is given by BS 7910 as follows:
ΔK th = 0.7 (5)
where the threshold in units of MPa√m for aluminium alloys is a constant
value at both positive and negative stress ratios. The requirement
stipulated in BS 7910 (in the chapter “Assessment for Fatigue”) is to
”use full stress range regardless of applied stress ratio (R )”.
The full stress range means σmax - σmin,
which corresponds to K max -K min. The definition of the threshold forR < 0 is ΔK th =K max - K min. The
thresholds ΔK th for the steels and aluminium
alloys given in BS 7910 are shown in Figures 1 and 2 as a function of
the stress ratio R .
The thresholds given by the WRC Bulletin, IIW and BS 7910 are stated as
constant values for R < 0.1 or R < 0,
as shown in Figures 1 and 2. However, the definitions of the thresholds
for R < 0 take two forms: ΔK th =K max - K min orΔK th = K max. The
expression by either ΔK th =K max - K min orΔK th = K max for R< 0 is significantly different from actual flaw evaluation
analyses. Below, the stress intensity factorsK max and K min are
investigated in detail using the stress ratio R =K min /K max and compared
with the thresholds given by the WRC Bulletin, IIW and BS 7910.