Page 69 - Reliability and Maintainability of In service Pipelines

58 Reliability and Maintainability of In-Service Pipelines

Wall thrust: Wall thrust failure is an ultimate structural failure with a limit
state function presented in Eq. (2.15).
GT a ; T cr ; tð Þ 5 T a tðÞ 2 T cr ð2:15Þ
The pipe capacity can be calculated using the following equation (Gabriel,
2011):
Þϕ
T a 5 F y W t 2 Δð ð2:16Þ
The threshold can be calculated from:

D o
T cr 5 1:31:67P s C L 1 P W Þ ð2:17Þ
ð
2
Fracture toughness: For localized stress concentration caused by defects, e.g.,
corrosion pits, a term stress intensity factor, K I , is used in fracture mechanics to
more accurately predict the stress state (“stress intensity”) near the tip of a crack
(caused by applied or residual stresses). It is a parameter that amplifies the effect
of stress field at the tips of crack leading to fracture. In essence, K I serves as a
scale factor to define the magnitude of the crack-tip stress field and is related to
the geometrical parameters and stress types of the element (Hertzberg, 1996).
In general, there are three deformation modes of fracture (Hertzberg, 1996):
(1) opening mode (Mode I); (2) in-plane shear mode (Mode II); and (3) out-of-
plane shear or tear mode (Mode III). Since Mode I is found to be the dominant
cracking condition in pipes under normal service conditions (Laham, 1999), most
of the time, only Mode I is considered in the failure analysis of the pipe (i.e., a
crack plane is perpendicular to the direction of the stress incurred).
If K IC is the critical stress intensity factor, known as fracture toughness,
beyond which the pipe cannot sustain propagation of the crack pit, the two limit
state functions for fracture toughness can be established as follows (Mahmoodian,
2013):

For axial fracture:G K IC ; K I2h ; tð Þ 5 K IC 2 K I2h ðtÞ ð2:18Þ
For hoop fracture:G K IC ; K I2a ; tð Þ 5 K IC 2 K I2a ðtÞ ð2:19Þ
In Eqs. (2.18) and (2.19) it is assumed that fracture toughness of the pipe
material is the same for both hoop and axial directions.
Laham (1999) presented a formula for stress intensity factor for a crack pit in
a pipe under hoop stress as follows:

3
p ffiffiffiffiffiffi X a 2c R
K I2h 5 πa σ i f i ; ; ð2:20Þ
d a d
i50