PSI - Issue 13

Konstantinos Kouzoumis et al. / Procedia Structural Integrity 13 (2018) 868–876 K. Kouzoumis et al. / Structural Integrity Procedia 00 (2018) 000–000

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2.1.2. Surface Flaws Calculation of reference stress in pipes with internal / external flaws is provided by equation P.18 of BS 7910:2013, which (with slight modifications) describes both internal and external flaws. As previously, through wall bending will be disregarded and the reference stress solution is expressed as, σ re f = 1 . 2 M S P m (7) Eq. (7) includes two multiplication factors, which are in direct correspondence to the ones in Eq. (1). The Folias factor is included in M S , which also accounts for the crack being surface-breaking rather than through-thickness, while the factor of 1.2, is given the same explanation as that given for through-thickness flaws. Concerning the latter’s history, the surface-breaking flawed flat plate solution in BS 7910 was based on the original work of Willoughby and Davey (1989), which certainly shows the existence of a safety factor of around 1.2 between the failure model and experimental data. It may be that this safety factor was treated as a “benchmark” and applied to surface flaws in pipes (for consistency with the behaviour of plates), leading to its later application to pipes containing through thickness flaws as well. 2.2.1. Through Thickness Flaws The API / ASME FFS procedure [API (2016)] calculates the reference stress in pipes with axial through wall (-thickness) cracks with the use of equation 9.C.47. This equation derives from the work of Miller (1988) and Willoughby and Davey (1989). The multiplication factor that translates applied stress to reference stress is stated to be “typically only applied to the membrane part of the reference stress because this represents the dominant part of the solution”. This explanation reinforces the simplification of disregarding through wall bending, and endorses the same simplification to be made here, σ re f = M T , i P m (8) M T , i , referenced as the “surface correction factor” in API (2016) is also a function of the shell factor ( λ ), while the i subscript concerns the fact that API / ASME provides four di ff erent formulae for the calculation of M T . From the four solutions, Eq. 9C.8 of the procedure is “recommended for use in all assessments” and will be implemented in the calculations. It should be noted that the shell factor / parameter ( λ ) in API / ASME is equivalent to the definition given by Folias, Eq. (4), with Poissons ratio ( ν ) set as 0.3. 2.2.2. Surface Breaking Flaws For surface breaking flaws, both a local and a global collapse solution can exist, in contrast to the through wall flaw where only net section (global) collapse can occur. In this respect, the API / ASME procedure provides two surface correction factors, one for local and one for global / net section collapse. Internal and external surface breaking flaws are not distinguished and are assessed with the same formulae. The simplified reference stress solution for surface breaking flaws, Eq. (9), which does not account for through wall bending, is the same as Eq. (8), with a di ff erence in surface correction factor which now relates to a surface flaw. As in the BS 7910 procedure, the through thickness flaw surface correction factor(s) are integrated in the formula of surface flaws with alterations to incorporate the di ff erent geometry. σ re f = M S P m (9) The surface correction factor for local collapse is, 2.2. API 579-1 / ASME FFS-1

B

1 M T , i

1 − C a

M L

(10)

B

1 − C a

s =

In Eq. (10) the through thickness flaw surface correction factor used ( M T ) for the calculations will be that of Eq. 9C.8 of API (2016), while the value of the parameter C will be set as 0.85.