PSI - Issue 75

10

Fabrice Deleau et al. / Procedia Structural Integrity 75 (2025) 392–418 Deleau Fabrice, Emmanuel Persent, Guillaume Coudouel, Guillaume Perrin/ Structural Integrity Procedia (2025)

401

The stress amplitude a  for metallic polycyclic fatigue being linked to the shear acting on a critical plane, according to (Lemaitre et al., 2020) and (Lu, 2002), the choice is based on the octahedral shear stress amplitude (i.e. the amplitude of so called Von Mises’s stress), the critical plane corresponding to the octahedral plane, according to (Dowling et al., 2007), (Lu, 2002), (Manin et al., 2010) and (Stephens et al. , 2000). This definition of stress amplitude is used for the so called Sines’s and Crossland’s criteria (Sines, 1981) and (Austin et al., 1965) for ductile materials, and is recommended by the API 17G, Annex D, 3 rd Edition (Stawaisz et al., 2014) and DNV RP C203, Section D standards (DNV GL RP C203, 2020). The stress amplitude a  depends on the amplitude stress state a  whose elements are

a ij  defined in equation (4):

max ij ij   −

min

2 (4) The scalar stress amplitude is based on Von Mises’s stress. It is given in equation (5), and its expanded form in equation (6): a ij  =

2 3 ( ) a J 

DNV   a

a = =

(5)

VM

1 2

(

) ( 2

) ( 2

)

( ) ( ) ( ) 12 2 2 23 13 a a a    + +

 

3     +

 

2

2

(6)

a 

a

a

a

a

a

a

=

      − + − + −

DNV

11

22

22

33

33

11

• Mean stress correction The mean (i.e. time-average) stress

m  acting on the fatigue lifetime of metallic material is a normal stress, and a positive stress (i.e. tensile stress) accentuates the damage by promoting the crack growth, and this is well documented (Dowling et al., 2007), (Lemaitre et al., 2020) and (Lu, 2002). DNV RP C203, Section D standard (DNV GL RP C203, 2020) recommends the use of a multiplicative factor 0.6 1.4 m f   to include the effect of mean stress, which is express in equation (7) : 0.8 1 0. 2 5 m m a f   = +           (7) Where the expression of m  will be set equal to DNV m  , given in equation (10). • Calculating the mean stress The exact definition of this stress, especially its orientation plane change from one author to another, depending on the nature of the stress state. (DNV GL RP C203, 2020) and (API 17G, 2019) propose a stress based on the mean hydrostatic stress (i.e. the mean normal stress acting on the octahedral plane) during the cycle m H  , and is given in equation (8) : (8) As the time-evolution of stresses is assumed to be linear and symmetric around their mean value, the mean stress state m  can be expressed in equation (9) : DNV H I       = = = + + 1 11 22 33 3 ( ) m m m m m m

max ij ij   +

min

(9)

m

ij 

=

2

So, the mean stress according to (DNV GL RP C203, 2020) can be developed as in equation (10) : ( ) min max min max min max DNV 11 11 22 22 33 33 m        = + + + + +

1 2

(10)