BWI fatigue life criterion

The BWI fatigue life criterion predicts fatigue failure in welded joints. The criterion takes into account local stress concentrations which may be due to the weld itself. The weld equation determines the number of cycles until failure occurs.

The BWI fatigue life criterion is based on the British Welding Institute's (BWI) formulation which uses the weld class as the basis for the fatigue life estimate. Because the BWI weld classes in this software are defined by the British Standard BS 5400, you need to be familiar with the weld class definitions to use the BWI fatigue life criterion accurately NOTE.

BWI criterion without mean stress effects

If you choose not to include the mean stress effects in the damage calculation, the BWI equation is written as NOTE:

where:

• Δσ1 is the maximum principal stress range.

• Nf is the number of cycles to failure.

• stdev is one standard deviation of the mean value of log10(Nf).

• a and m are parameters dependent on the weld class you specify.

• d is the number of standard deviations. You can specify the number of standard deviations or the probability to failure, Pf. The number of standard deviations and the probability to failure are related by the following equation:

The erf function is the Gauss error function that is defined as:

The following table gives the values for the parameters a and m and the value for the one standard deviation of the mean value of log10(Nf) for the available BWI weld classes.

BWI weld class	log10a	stdev	m
N/mm2	N/m2
B	15.3697	39.3684	0.1822	-4.0
C	14.0342	35.0330	0.2041	-3.5
D	12.6007	30.6017	0.2095	-3.0
E	12.5169	30.5176	0.2509	-3.0
F	12.2370	30.2379	0.2183	-3.0
F2	12.0900	30.0881	0.2279	-3.0
G	11.7525	29.7489	0.1793	-3.0
W	11.5662	29.5615	0.1846	-3.0

The nominal fatigue strength decreases from class B through class W as shown in the following figure.

S-N curves for BWI weld classes with d=0

The mean value refers to the average Welding Institute equation for a specific weld class. The equation for each weld class is a curve fit of empirical data. Therefore, some of the data lies above this mean curve and some lies below. If you reduce the curve by a number of standard deviations, you make the resulting curve more conservative. Typically one or two deviations below the mean are sufficient. Two standard deviations below the mean are typically used for design situations. This suggests that 98% of the parts will achieve the predicted life.

BWI criterion with mean stress effects

If you choose to include the mean stress effect in the damage calculation, the software uses one of the following methods to update the S-N curve by including the mean stress in the BWI equation:

• Goodman method

• Soderberg method

• Gerber method

• Morrow method

where, in addition to the variables defined for the BWI equation:

• σm is the mean stress of the cycle along the principal axis.

• Su is the ultimate tensile strength material property.

• Sy is the yield strength material property.

• σ’f is the fatigue strength coefficient material property.

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BWI fatigue life criterion, Simcenter 3D 2021.1 Series

© 2020 Siemens

Stephens et al., “Metal Fatigue in Engineering”, 1990, pp. 415-416.

Gurney, T. R., “Fatigue Design Rules for Welded Steel Joints”, Welding Institute Research Bulletin, Volume 17, No. 5, May 1976, pp. 115-124.

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