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.