PSI - Issue 14

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

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Such a function was earlier offered by McEvily (1991):

ka e a     ( ) 1 . We have found that another equation is more suitable for this modeling: k a e a     ( ) 1 .

(16) Coefficient k can be determined from (15), (16) as a limit case: at a  0 the fatigue limit σ r for unnotched specimens correlates with K th value:       / 2 th K k r r . It is noted that for different pairs of σ r and ( K th ) r referring to different r , similar k values increasing from 4 mm -0.5 up to 6 mm -0.5 are obtained for the corresponding increase of the yield stress of metal from 600 up to 1100 М P а . Physically k might be interpreted as a parameter accounting for the reference structural size of a material d (several grain sizes) within which a fatigue crack transfers from a shear stage to a macro stage of extension, d  1/ k 2 . Assessment made using the formulae (14), (15) with a 0 varied from 0 to 0.1mm allows to predict a simultaneous effect of cyclic asymmetry, presence of corrosion medium and surface quality on the fatigue limit. In case of corrosion influence ( K th ) 0 = 0 is accepted. The surface quality has been accounted for in assumption a 0 = R z . The dependence N i (  σ ) for a certain welded joint has been obtained in the following conditions:  Technological stress concentration in WTZ was taken into account at numerical integration (10) by a function (7),  Structural stress concentration was considered by multiplication of  σ by K s ,  Actual r value was found accounting for an action of inherent and reactive residual stress (initial level or reduced values after pressure test or additional treatment) . Figure 7 shows an example of calculated curves N i (  σ ) for welded joints in the “as - welded” state for different K w values (independent on design stress asymmetry), and for welded joints with reduced σ res level loaded in compression. When an actual r value exceeds 0.5, the calculated effective stress concentration factor is close to its theoretical value; essential differences between them take place at a lowered r .

Figure 7 – Calculated dependences N i (  σ ) for different Kw values indicated for each curve. We lded joints in the “as - welded” state (a) and after simulated pressure test and compressive design load (b) On the basis of similar serial assessments it is possible to make some generalizations reducing the procedure of N i estimation to the following formula (“base curve”), where parameters depend on loading medium and actual local r i value in a concentrator: