PSI - Issue 60

D. Sen et al. / Procedia Structural Integrity 60 (2024) 44–59 Deeprodyuti Sen/ Structural Integrity Procedia 00 (2024) 000 – 000

57

14

3. For both flaw geometries (BPFF and DFF), the allowable nominal stress exhibits a saturation tendency at higher flaw lengths. This is essentially a consequence of the stress concentration factor ( k t ). In this study, cracks of the axial length up to 100 mm are considered. 4. As expected, the presence of residual stress has a significant influence on the allowable flaw size. Detailed calculations accounting for the relaxation of residual stresses are, however, required for a more realistic assessment.

Appendix A.1. Calculation of stress concentration factor, ‘k t ’ , for Debris Fretting Flaw (DFF)

In contrast to the case of BPFF, a closed-form equation for evaluation of for a DFF is not provided in the CSA Standard (2016). It, however, suggests a general procedure for estimation of using a relation between stress concentration factor (SCF) and stress intensity factor K (SIF). The evaluation of ‘ k t ’ for a DFF, therefore, can be obtained from the following relation CSA (2016) (is referred to as k t3D for DFF here).

3 G I D      F K

   

2

1   

k

3 t D



n

where

2 t D K        2 I D 1 k

F



G

   

2



n

Thus, the stress concentration factor for a three dimensional flaw can be calculated provided stress concentration factor for the 2-D case and stress intensity factor for both 2-D and 3-D cases are available. Calculation of 2-D Stress Concentration Factor The 2-D profile of a DFF is parameterized by its in-plane dimensions, that is, flaw tip root radius ρ and radial flaw depth ‘a’. The expression for 2 -D stress concentration factor proposed in Pilkey (1997) is as follows, 2 ( , ) 0.855 2.21 t D a k a     Calculation of 2-D Stress Intensity Factor The equation for stress intensity facto r for a ‘long’ axial flaw is taken from Zahoor’s Handbook (1991). It is given in the following equation, 2 2 2 2 ( ) 2 ( ) o I D r o i R K a p aF R R    2 4

0.25 1.1 [4.951( / ) 1.092( / ) ] [0.2( / ) 1] i a w  

F A a w A R w   

Calculation of 3-D Stress Intensity Factor An analytical equation for evaluation of stress intensity factor for a part-through wall crack under internal pressure is given in the CSA Standard (2016) and can be expressed as,