PSI - Issue 75

12

Deleau Fabrice, Emmanuel Persent, Guillaume Coudouel, Guillaume Perrin/ Structural Integrity Procedia (2025)

Fabrice Deleau et al. / Procedia Structural Integrity 75 (2025) 392–418

403

state, it is proposed to consider the highest tensile stress during the cycle, i.e. the maximum principal stress I  . The mean stress is thus the mean value of the peak normal stress, i.e. the stress projected onto the direction of max I  , which corresponds to the highest eigenvalue of max  . As previously analysed, firstly, the stress triaxiality 0.66   during the cycle, which denotes an equi-bi-tension state, i.e. the same conditions of (Gaur, 2016), and secondly, the highest principal stress I  is always positive, so it can be used as reference for mean stress for the Gerber’s correction. As the stress state follows a non-proportional evolution, API 17G, Annex D, 3 rd Edition (Stawaisz et al., 2014) recommends the following method. First, The diagonalization of max  provides its eigenvalues max max max I II III , , ( )    and their respective eigenvectors max max ma II I I x I I ( , , ) n n n , with max max max I II III      . As max I  is the maximum tensional stress during the cycle, the normal stress acting on x I ma n shall be the reference for the definition of mean stress, which is thus the projection of the stress state ( ) t  onto x I ma n , as defined for a cycle duration T in equation (15) : max ( )  =   n I (16) The time-evolution of stresses is assumed to be linear and symmetric around their mean value, the mean value can be directly obtained by the average of max I  and min I  , which is given in equation (17) from equation (18) : max min max min I I I n n   =   (17) And the mean stress is simplified as in equation (18) : max min I I I 2 m m P     + = = (18) I I ( ) t t n  max I  I  1 ( )d m T t t T =  (15) With I ( ) t  denoting the normal stress acting on x I ma n at time t , defined as in equation (16) :

• Corrected stress amplitude The corrected stress amplitude

a P  is calculated in the same way as in the (DNV GL RP C203, 2020), but using the

Gerbers’s mean stress correction factor G k given in equation (14). It is shown in equation (20):

k

(20)

a f   = G a P

DNV

x

2.6. SN curves SN curves are obtained by experimental testing (e.g. following the prescribed ASME or DNV code procedures) or by using directly the SN curves given by (DNV GL RP C203, 2020) which provides design S-N curves in air and seawater with cathodic protection for base material of high strength steel subjected to a high mean tensile stress. The S- N curve “BM3” is applicable for steel forgings having a yield strength above 80 ksi. This fatigue curve could be used for the ASTM 182 F22 forged material of the i-Clip connector which has a minimum yield strength of 93 ksi. It should be noted that the design S-N curves are based on the mean-minus-two-standard-deviation curves and are therefore associated with a 97.7% probability of survival. They are given for a high mean tensile stress without specifying the value of this stress.