PSI - Issue 75

9

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

400

- The stress amplitude will consider those two stress states, because the distance between stress states ( ) 2 1 2 ) ) ( ( t J t   − is maximum for max 1 ( ) t   = and min 2 ( ) t   = . - The temporal evolution of the stresses between those states is linear and symmetric around a mean (time average) stress state called m  , which then can be directly calculated as the average between max  and min  . - The highest principal stress, called I  , is always positive. - The stress state is close to equi-bitension during the whole cycle, because the stress triaxiality  varies between 0.6 and 0.7. • Calculating the stress range According to fracture mechanics theory, materials break when enough stress and energy are applied at the atomic scale, causing the bonds between atoms to rupture. The most common loading leading to crack propagation is opening (Mode I), which occurs under a positive principal stress for a given stress state. Considering this perspective, (API 16F, 2022) standard recommends that the stress amplitude to be considered in fatigue life analysis be the half of the maximum positive principal stress of the stress range tensor, which is denoted   . This stress range represents the loading state difference between the two stress tensors max  and min  (equation (1)) corresponding respectively to the maximum loading instant max ( ) t F F = and the minimum loading instant min ( ) t F F = . max min    −  = (1) This stress state difference can be represented by its eigenvalues I   , II   , and III   (eigen stress ranges), and the characterizing stress range is thus the maximum positive eigenvalue of   , (i.e. its spectral radius), which corresponds to the first one because of the evolution of stresses observed previously. So, the stress range is expressed in equation (2). ( )   API I I,II,III max k k      =  =  =  = (2) 2.3. Calculation of the amplitude stress according to (API 16F, 2022) This methodology is fully based on the recommendations of (API 16F, 2022).

• Calculating the amplitude stress The stress amplitude API

a  is then the half of the stress range (equation (3)):





a

(3)



=

API

API

2

2.4. Calculation of the amplitude stress according to DNV-RP-C203 This methodology is fully based on the recommendations of (DNV GL RP C203, 2020), Section D.2.1 standard, but some aspects of it can also be found in API 17G 3 rd Edition standard (Stawaisz et al., 2014).

• Calculating the stress amplitude