The fatigue strength estimation method, based on nominal stresses, has already been in use for almost 150-years. The nominal stress method is the most used and the simplest method for estimating the fatigue life durability of as-welded state structures. [79]
The nominal stress approach is based on the large number of fatigue test results for different kind of details. These can be divided into two categories: single details and assemblies, see Fig. 20. E.g. in SFS-EN 1993-1-9 is given FAT-class over 70 details and only two of these deal with thermally cut edges. The statistical analyses are used and results have been published in so called FAT classes in official codes and standards [80, 81].
Fig. 20 An example of detail categories in prEN 1993-1-9:2003. On left side is a typical detail for a gas cut plate and on the right is an example of a complicated detail Tube socked joint [78].
The basic idea is that the fatigue strength forecast is based on the detail defined nominal alternating stress, which is compared with the detail's design-class (FAT-class). Simple linear elastic theory is used in stress calculations. The local stress raising effects such as the welds detail and the attached plates are not necessary to take account in the stress calculations, as these effects are already included in the FAT cases. If the selected FAT class does not include a stress raising effect that will appear in a real structure, the effect must be included in the general stress calculation.
The fatigue classes based on the nominal stress are available in most design codes and guidelines, such as EN13001-3, SFS2378, IIW XIII-1965-03, EN 1993-1-9 and ISO 10721-1. The nominal stress method is the only method which has been presented in the design standards for estimating the fatigue strength of thermally cut edges. In the
standards classes values variety between FAT 80 to FAT 280 MPa. The FAT-classes depend on cut method, surface quality, starting points, manufacturing process and material yield strength. In
Table 6 was collected some general used fatigue classes of the thermal cut surfaces.
EN13001-3 was only standard that gives fatigue classes in function of yield strength of cut material. In Fig. 21 was presented how the fatigue class depend on yield strength of the material. The slope of the SN-curves is normal m = 3 and some cases it is m = 5.
The used probability of FAT classes varies in different design standards. The normal probability rate is between 95% and 97.7% and normal used confidential interval is 75%. [4, 5, 78, 82, 83, 84]
Table 6. Some FAT-classes for flame cut edge.
Standard FAT m
EN13001-3-1-2012 140 5 Independent of yield strength 140-180 5
Depend on yield strength
Edge quality in accordance with Table 5 Range 3 of EN ISO 9013:2002
160-280 5
Depend on yield strength
Edge quality in accordance with Table 5 Range 1 of EN ISO 9013:2002
IIW:
XIII-1965-03/XV-1127-03: 80-125 3 Independent of yield strength
Depends on quality and cutting method.
EN 1993-1-9:
125-140 3
Independent of yield strength Depends on quality and cutting way (manually or machine controlled) ISO 10721-1
125-140 3
Independent of yield strength
Depends on quality and cutting method (manually or machine controlled) SFS-ENC
1993-1-1:1992 125-140 3
Independent of yield strength
Depends on quality and cutting method (manually or machine controlled) SFS2378
112-125 3 Independent of yield strength Depends on quality
Fig. 21 Commonly used FAT-classes as a function of material yield strength. Range means the quality of the edge according to EN ISO 9013:2002.
The calculated fatigue strength in different stress range levels can be calculated with a simple Eq. (35). The slope of the curve varies from m = 3 to m = 5. Eq. (35) is valid when the nominal stress range is smaller than 1. 5 ∙ , as both compress and tensile stress are equally effective.
106
2 )
( ∆ ⋅ ⋅
= m
f FAT
N σ
(35) The general assumption in fatigue strength assessment of welded structures is high residual stresses have significantly influence on their fatigue behaviour. It means that when nominal loading on a structure is compressive, the actual residual stresses may result in local tensile stress near the location where a fatigue failure is probable to occur [85].
Fig. 22 R-values.
The recommendation for correction factors f(R) for fatigue loading is presented in the IIW document [5], when the stress ratio is R < 0.5. The fatigue strength correlation can be use by multiplying the basic fatigue class of details by f(R), Eq. (36). The value of the fatigue class correlation factor depends on the value and direction of residual stresses. The structure complexity has also influence on the correlation factor. The correction factor calculation rules are presented in Fig. 23. The low residual stress enhancement factor should be used when residual stresses are below 0.2 times the material yield strength [5]. Short welds and thermally cut edges should be used as a middle residual stress assumption and a high residual stress curve should be utilized for complex structures [5].
FAT R f
FATR = ( )⋅ (36)
The design code EN1993-1-9 also gives some guidance to take account of the mean stress influence on the fatigue strength. In non-welded details and stress-relieved welded details, the mean stress influence on the fatigue durability can be taken into account by using a reduction factor of 0.6 applied to the compressive part the stress cycle. The reduction equation is
min max 0.6 σ σ
σ = − ⋅
∆ (37)
If the plastic strains are small, The Smith, Watson and Topper equation also gives a simple correlation factor. To make an assumption, the reference case Rref = 0 can be written Eq. (38) where the square root term is correlation factor that depend on stress ratio Rtrue [87, 88].
true Rref
Rtrue =∆ ⋅ −R
∆σ σ =0 1 (38)
Fig. 23 The f(R)- functions.