INTRODUCTION
Failure due to corrosion has been one of the greatest concerns in maintaining
the pipelines integrity. As the pipeline infrastructure ages, metal loss due
to corrosion represents a major source of material degradation in steel pipes
which most often reduces its burst strength with increased potential for catastrophic
failure. Corrosion is a time dependent electrochemical process and depends on
the local environment within or adjacent to the pipeline (Cosham
and Kirkwood, 2000). At the points where corrosion occur the wall of the
pipe become thinner, leading to loss of its mechanical resistance. Therefore,
the continual service of corroded pipelines must be guaranteed by Fitnessforservice
(FFS) assessments.
FFS decisions are made based on prediction of the residual strength of the
corroded pipeline (Escoe, 2006). Methods for assessing
corrosion metal loss defects have been available for many decades, as for instance
the NG18 equation and ANSI/ASME B31G code. Throughout the years many modifications
were made to the original equations and many newer methods like ASME B31.G (ANSI/ASME,
1991), Modified B31G (KAPA, 2000), RSTRENG (Kiefner,
2006), DNV RPF101 and several inhouse codes were adopted.
Although, these widely used acceptance criteria simplify the integrity assessments
of inservice pipelines, they are known to be conservative (Belachew
et al., 2009a) and thus enforce premature retirement of pipelines.
Therefore, pipeline operators need reliable defect assessment method not only
to assure safe operation but also to implement optimum operation cost. Motivated
by these observations, in the recent years various alternative assessment methods
have been developed mostly based on finite element studies and burst test results.
Modern numerical analysis methods have enabled the modelling of realistic defect
shapes and nonlinear material behaviour (Lee and Kim, 2000).
Conventional procedures used to assess the integrity of corroded piping systems
with axial defects generally employ simplified failure criteria based upon a
plastic collapse failure mechanism incorporating the tensile properties of the
pipe material (Chiodo and Ruggieri, 2009). In this paper
the finite element simulation of various corrosion defects are presented. A
central focus is to gain insight into the effects of defect depth, defect extent
and defect width on the burst strength of the pipeline. Stressbased criterion
based on plastic instability analysis was used to predict the failure pressure
(Belachew et al., 2009b). During the simulation
of nonlinearities due to plasticdeformation and largedeformation were considered.
The results were compared with the predicted burst pressures using some of the
commercial codes.
Consideration of nonlinearities: During failure simulation the pipeline
materials are subject to irreversible structural deformation due to loading
beyond the material’s yielding point. Therefore, the nonlinear stressstrain
relationship and the changes in geometry due to large displacements require
a nonlinear structural analysis. These structural nonlinearities are usually
know as materialand geometric nonlinearities. The geometrical nonlinearity
is associated with the necessity to updating the coordinates of the initial
and final states of deformations during the finite element simulations. True
stress and true strain material properties based on incremental plasticity approach
is used expression the material properties (ANSYS, 2009).
To accurately predict the behaviour of a corrosion defect, the material behaviour,
in particular the plastic behaviour must be modelled appropriately. The finite
element model allows the material behaviour to be modelled with a uniaxial true
stressstrain curve as mentioned in Fig. 1. The use of truestress
versus truestrain data allows an incremental plasticity scheme to be used which
can account for strain hardening and subsequent unloading, but requires a significant
increase in computing resources (Chouchaoui, 1993). If
the stresses increase monotonically and significant unloading does not occur,
the stressstrain behaviour of typical pipeline materials can be modelled with
deformation plasticity theory using the RambergOsgood Eq. 1
to represent the true stressstrain curve (Ramberg and Osgood,
1943):
Pipeline steels typically display anisotropic yield behaviour as a result of
the rolling process used to create the steel plate from which the pipe is manufactured.
For the analysis of corroded pipe, it is recommended to use the material properties
in the circumferential direction since this is the direction of maximum principal
stress in plain pipe (Chouchaoui and Pick, 1996).

Fig. 1: 
Tensile properties of the API X52 grade steel (DNV,
1997) 
FINITE ELEMENT METHOD
Analysis procedures: The solution to the nonlinear governing equations
can be achieved through an incremental approach. The incremental form of the
governing equations can be written as shown in Eq. 2 (Zienkiewicz,
1971):
where, Δu is unknown incremental displacement vector, is ΔP unknown
incremental applied load vector.
The solution is obtained by taking a series of linear steps in the appropriate direction in order to closely approximate the exact solution. When solving nonlinear problems, ANSYS^{®} uses the NewtonRaphson (NR) method, which involves an iterative procedure. This method starts with assumed solution and determines the magnitude of the increment as mentioned in Eq. 3 and 4, respectively. The corresponding outofbalance load vector, which is the difference between the applied loads and the loads evaluated based on the assumed solution is calculated as enlisted in Eq. 5:
In order to satisfy the equilibrium conditions exactly, the outofbalance
load vector must be zero. However, as the nonlinear equilibrium conditions are
solved approximately, a tolerance is introduced for the outofbalance load
vector in order to terminate the solution procedure. In each iterations, the
NR method computes the outofbalance load vector and checks for convergence
based on the specified tolerance. If the convergence criterion is not satisfied,
the trial solution is updated and based on the calculated incremental displacements,
the next incremental solution vector is determined as dipict in Eq.
6 and 7 leading to the computation of the new outofbalance
load vector as mentioned in Eq. 8:
This procedure is repeated until convergence is accomplished. There are also options like time stepping, a bisection method and line search algorithm methods for improving the convergence in ANSYS^{®}.
Element type: In this study, higher order 8node solid elements (SOLID45)
were used to analyse the 3D models. Accurate application of the finite element
method involves the use of a large number of 3D solid elements to correctly
model the corrosion geometry and the use of large displacement, elasticplastic
analysis to model the material response (Cronin, 2000;
Szary, 2006). Two layers of elements were used through
the remaining ligament of each corrosion defect. The element type chosen allows
both material nonlinearity and large localized nonlinear deformation to be
performed (ANSYS, 2009).
Boundary conditions and loading: The symmetries of boundary conditions, as mentioned in Fig. 2, were used in order to reduce the size of the models and hence reduce computer run times. Coarser meshes are used farther from the defect location to reduce the nodes number. Constraints were also applied to the models to eliminate rigid body motion. The model was extended far enough from the defect location to ensure the boundary conditions did not affect the results of the analyses. Internal pressure loading was applied to each model and automatically increased during the FE analysis. Tensile axial loads were applied at the ends of the pipe in order to simulate the endcaps during burst test.
Failure criteria: Failure may be defined as a limit above which material
fails. It may occur as a fracture, excessive deformation or when an arbitrary
set value of stress, strain or energy is reached.

Fig. 2: 
Finite element model of the defect and mesh close view 
Corrosion defects are relatively smooth and pipe materials are generally tough,
therefore, the failure of the corrosion defect is usually by plastic collapse
of the defect ligament as opposed to low ductile fracture (Chouchaoui,
1993). Observations of the corroded material in the vicinity of the failures
show a significant amount of plastic deformation and localized necking indicating
that the initial failure occur by plastic collapse. The contours of the grain
structure in the vicinity of the failure show a significant localization of
the deformations at the failure location (Cronin and Pick,
2002).
Finite element analysis of pipe with corrosion defects do not in itself predict
the failure pressure of the pipe since it is impossible to predict local instability,
such as necking, which usually leads to ultimate failure. Thus, there should
be defined criterion to decide the failure point during simulation. In this
work, the twocriterion approach, stressbased and instability based criteria
was used to locate the failure points (Chouchaoui, 1993).
This approach involves the calculation of a critical stress or strain value
according to the stressstrain curve of the material. Plastic collapse is deemed
to occur either when the equivalent stress exceeded the critical stress through
the entire thickness of the ligament or when the gradient of plastic strain
through the entire ligament becomes constant and the plastic strain increase
asymptotically.
The critical stress is defined as the ultimate tensile stress from the true stressstrain relationship. Among the different failure theories ANSYS^{®} uses the von Mises criterion. For pipe calculation it is more convenient to use this theory with cylindrical coordinates, where stress components are combined into one effective stress as enlisted in Eq. 9:
Where:

: 
Axial stress 

: 
Tangential (hoop) stress 

: 
Radial stress 

: 
Equivalent (von Mises) stress 
RESULTS AND DISCUSSION
The models were developed from API X52 steel with nominal dimensions of 274
mm diameter, 12 mm wall thickness and 600 mm section length. These models were
selected to cover the following basic parameters: normalized defect depth (d/t
of 0.10, 0.20, 0.40, 0.50, 0.60, 0.75, 0.80 and 0.90, normalized defect extent
(L/D of 0.20, 0.40, 0.60, 0.80, 0.94, 1.00, 1.20, 1.40, 1.60, 1.80 and 2.0 and
normalized corrosion width (w/t of 1.0, 2.0, 3.0, 5.0, 10.0 and 15.0). For the
full matrix of the pipe and defect dimensions given above, a total of 29 models
with internal defect were generated. One more model with an external defect
was developed to compare the effect of similar defects on the external and inner
surface of the pipeline. For convenience all the predicted failure pressure
is normalized with the failure pressure of an intact pipe according to maximum
hoop stress theory as mentioned in Eq. 10:
With the increase of internal pressure, the stress variation through the ligament
exhibits three distinct stages; elastic deformation, plastic deformation and
material hardening. This phenomenon is justified by various researchers (Fu
and Kirkwood, 1995, Choi et al., 2003, Lee
and Kim, 2000. The stress distribution through the ligament is dipicted
in Fig. 3.
• 
Elastic deformation: A linear response progressing
to a point when the elastic limit is reached 
• 
Plastic deformation: Plasticity spreads through the ligament (the
von Mises equivalent stress increases very slowly because of the constraint
of the surrounding pipe wall) 
• 
Material hardening: The whole of the ligament deforms plastically
but failure does not occur because of material work hardening. Failure of
the defect pipe was deemed to occur when the minimum von Mises equivalent
stress in the ligament was equal to the true ultimate tensile strength of
the material. At this stage the plastic strain increases drastically as
drawn in Fig. 4, which confirms structural instability 
Figure 5 illustrates the effect of defect depth on the burst strength by using four commercial codes and FEM. As the defect depth increase, the burst strength decrease. The predictions by the commercial codes showed conservative estimation brust of the strength. On average deviation of 44% for B31 G, 21% for Modified B31 G, 16% for DNV, 31% for RSTRENG and 21% for PCORRC were observed as compared to the FE results.
Figure 6 illustrates the effect of longitudinal extent of
the defect on the burst strength by using four commercial codes and FEM. As
the defect length increases up to about the size of nominal diameter, the burst
pressure Nov. 3, 2010 decreases.

Fig. 3: 
Von Mises stress distribution through the ligament 

Fig. 4: 
Von mises plastic strain distribution through the ligament 

Fig. 5: 
Effect of defect depth on burst strength 
Further increase of the defect length has insignificant effect on the burst
strength. Similarly, the commercial codes showed conservative estimation. On
average deviation of 33% for B31 G, 19% for Modified B31 G, 11% for DNV, 27%
for RSTRENG and 17% for PCORRC were observed as compared to the FE results.
Figure 7 illustrates the effect of defect width on the burst
strength of pipelines using FE simulation. It was observed that a defect width
more than four times the nominal wall thickness has insignificant effect on
the burst strength.

Fig. 6: 
Effect of defect extent on burst strength 

Fig. 7: 
Effect of defect width on burst strength 

Fig. 8: 
Effect of equivalent defect on the internal or external surface 
Therefore, the fact that excluding the effect of circumferential extent of
the defect in commercial codes is justifiable for defects wider than four times
the nominal thickness of the pipe.
The effect of equivalent defect located on external and internal surface of
the pipe were evaluated for the critical nodes as shown in Fig.
8. The von Mises plastic strain and von Mises stress distribution through
the ligament is shown in Fig. 9 and 10,
respectively.

Fig. 9: 
Von Mises plastic strain distribution through the ligament 

Fig. 10: 
Von Mises stress distribution through the ligament 
The result certify that, the location of the defect have no significant effect
on the burst strength analysis.
CONCLUSION
Simulation results of various corrosion defects were presented. The effects of defect depth, defect longitudinal and circumferential extent on the burst strength of the pipeline were studied. Stressbased criterion based on plastic instability analysis was used to predict the failure pressure. During the FE simulation the nonlinearities due to plasticdeformation and largedeformation were considered. The results were compared with the predicted burst pressures using some of the available commercial codes. The following observations were forwarded:
• 
Available commercial codes for pipeline capacity assessment
are conservative 
• 
As the defect depth increase, the burst strength of the pipe decrease
more or less in a linear manner 
• 
The effects of an infinitely extended longitudinal defect can be approximated
by an equivalent defect length equal to pipeline nominal diameter 
• 
The effects of circumferentially extended defect more than four times
the pipeline nominal thickness can be approximated as defect having width
equal to four times the nominal pipeline wall thickness 
• 
Circumferential extent of defect less than two times the nominal pipeline
wall thickness need special attention due to excessive stress concentration 
• 
Equivalent defect on the internal or external surface of the pipe have
approximately similar effect on the burst strength of the pipe 