PSI - Issue 14

Ilyin A.V. et al. / Procedia Structural Integrity 14 (2019) 964–977 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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Calculation of N c 0 as a result of integration of (10) in the limits from a 0 = 3 mm to a max has no theoretical issues. But the estimation of N i 0 is more complicated as it should be related to the physics of multi-stage damage process in the stress concentration zone of both design and residual stress. The first step may be done on the basis of K w determination for typical welded joints. If we recon the value  in the formula (3) as unknown parameter, we could compare the calculated A values for each fatigue strength class of welded joints mentioned in the standard document DNVGL-RP-C203 at a reference thickness with its fatigue limit at 10 7 cycles as suggested by Ilyin and Sadkin (2013). This procedure tells that the results of such a comparison may be approximated by the formula (13) Here an “effective” radius  ef is close to 1.0 mm that is a mean  value for welded joints in the “as - welded” state. Hence, an S-N-curve method is fully equivalent to the fatigue strength assessment with the use of a unified “base” curve and stress concentration factors found from interpolation formulae taking  ef = 1 mm. The base curve corresponding to K w = 1 is determined by the parameters: lg  = 12.91, q = 3.0 for loading in air, and lg  = 12.43, q = 3.0 for loading in a corrosion medium. An advantage of such a modification of S-N-curves method is an opportunity to take into account without empirical corrections all the factors influencing on stress concentration: thickness of welded parts, weld geometry, type of loading. For welding processes allowing to attain an improved weld geometry (for example, TIG), the corresponding value  ef should be used that expands the opportunities given by the calculation method. It is obvious that the position of base curves reflects the combined effect of as-rolled surface and extreme high cyclic asymmetry. That is why the change of r should change the slope of the base curve. The next step is a transition to the quantitative modeling of the process. Preliminarily notes are:  Practical coincidence of the exponent q in a cyclic crack resistance diagram (10) and the exponent m in a base S-N-curve (1),  Practical independence of failure stress in the high-cycle loading area on the yield stress of steel that is typical for fatigue crack kinetics. Both these facts confirm that the position of S-N - curves for welded joints is almost determined by the cyclic life at the stage fatigue cracks propagation. Hence, it is possible to accept      c a a ef i f K da N 0 . (14) Here a c = 3 mm, f (  K ef ) is an analytical approximation of the cyclic crack resistance diagram. There are different propositions on initial crack size a 0 in the literature, from 0.10 up to 0.50 mm. There are some reasons for the benefit of a 0 = 0.1 mm:  First, thermal erosion flaws of the depth 50...100  m such as oxide films implanted into base metal at grain boundaries are typical for as-rolled surface,  Second, FEM calculations show that at this distance from the surface a crack of initial half-round shape nucleating from a “point” -type sharp concentrator with  = 0 has K I value not exceeding the same for a crack located along the weld at its toe and extending from a blunt concentrator of the mean  = 1 mm. Hence an assumption that a 0 = 0.1 mm in fact takes into account an actual variation of WTZ micro geometry allowing to use the mean  value in estimation. However such a crack depth is within the range o f “physically short” ones, and a function in the denominator of integral (14) should have a more complex kind: , , ) ( f K r a  . Peculiarities of short cracks are reduced to the decrease of crack closure effect, its complete absence at a  0 and gradual increase during a crack growth from the micro to macro size as presented by McEvily (1991), Navarro and De Los Rios (1987). It corresponds to the physics of initial stage of fatigue when a micro crack extends in the plane of the maximum shear strain independent on load sign. The second feature is a non-zero rate of damage propagation even if a  0. These features may be modeled by introduction a function f ( a ) into formulae (11a – 11b) which tends to zero at a  0 and is equal to 1 for a macro crack:   (1 0.75 ) ( ) th 0 r a K K K ef         for r ≥ 0, (15a)   ( ) (1 0.77 ) 0.77 (1 0.5 ) th 0 a r r r K K K K ef              for r < 0. (15b) ef K A    1 w .

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