Volume 20 Preprint 71
Residual strength analysis of steel pipeline with inner and outer defects
C.J. Han, S.S. Tan, C. Yu and J. Zhang
Keywords: corrosion defect, FEM, failure stress, defect alignment
Corrosion is the mainly effective factor considered as the most threatening element on the transition pipeline and play integral part in residual strength assessment and corrosion allowance design of transition pipeline. Improved ASME B13G method is most widely used. This paper focuses on the pipeline with corrosion defects inside and outside at the same time using nonlinear finite element method analysis, compares simulation results to the theoretical results. Furthermore, this paper investigates its mechanical behaviors and stress-strain distribution regular through simulation on the basis of corroded pipeline with single corrosion defect, predicts accurate residual strength and increasing tendency under different inner pressure, illustrates the failure pressure of transition pipeline with corrosion defects with different interactional location. Stress concentration appears on the edges close to the center of inner corrosion defect and finally expands to the whole defect area circumferentially. Maximum stress and plastic strain occur at the defect center to cause pipelineâ€™s failure. Changing rate of stress will increase rapidly under inner pressure once the overlapping region grows and strain will reach higher value after stress exceeds the yield point.
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Residual strength analysis of steel pipeline with inner
and outer defects
C.J. Han1, S.S. Tan1, C. Yu1, J. Zhang2*
1.School of Mechatronic Engineering, Southwest Petroleum University,
2. State Key Laboratory for Strength and Vibration of Mechanical Structures,
Corrosion is the mainly effective factor considered as the most threatening
element on the transition pipeline and play integral part in residual strength
assessment and corrosion allowance design of transition pipeline. Improved
ASME B13G method is most widely used. This paper focuses on the pipeline
with corrosion defects inside and outside at the same time using nonlinear
finite element method analysis, compares simulation results to the theoretical
results. Furthermore, this paper investigates its mechanical behaviors and
stress-strain distribution regular through simulation on the basis of corroded
pipeline with single corrosion defect, predicts accurate residual strength and
increasing tendency under different inner pressure, illustrates the failure
pressure of transition pipeline with corrosion defects with different
interactional location. Stress concentration appears on the edges close to the
center of inner corrosion defect and finally expands to the whole defect area
circumferentially. Maximum stress and plastic strain occur at the defect center
to cause pipeline’s failure. Changing rate of stress will increase rapidly under
inner pressure once the overlapping region grows and strain will reach higher
value after stress exceeds the yield point.
Keywords: corrosion defect, FEM, failure stress, defect alignment
With global economy developed, world’s demand for energy especially the oil
and nature gas becomes more and more urgent. Transition pipeline comes to
be an indispensable part in petroleum industry. For the aim of safety, saving
money and time, reducing human cost, assurance of transition pipeline is
valued seriously. Pipeline’s invalid elements include erosion, material failure,
earthquake, solid impact and so on, among them corrosion defect is the most
involved problem the transition pipeline faces in the actual working situation.
Eventhough well measures of erosion-protection are taken on transition
pipeline, it will damage in complex occasions with service time and failure of
anti-corrosion coat gradually. Corrosion divides into location types inside and
outside the pipeline, uniform and local types based on the failure form, single
and group types based on the corrosion amount.
In the past, in order to avoid disasters caused by the failure issues such as
leakage and great deformation, transition pipeline is always investigated in
empirical formula to predict the failure stress. In recent years, finite element
method and numerical simulation model are gradually implied on pipeline with
single defect mostly.Both the industry model, i.e., ASME B13G, modified
B13G and DNV models, and the FEA model developed in this work predict that
the failure pressure of a pipe with corrosion defects
B13G is mostly widely
paper studies the pipeline with two
interactional corrosion defects inside and outside the pipeline at same time,
displays the distribution of Von Mises stress of the pipeline with different
defects locations. The failure stress is also compared according to the
occasions of the defects.
2 Theoretical method and numerical simulation model
2.1 Assessment method
There are so many methods to describe the mechanical behaviors of
transmission pipeline, improved ASME B13G is:
L ≤ √50Dt
L > √5045
M$ = [1 + 0.6275 +, − 0.003375 /+,0 ]
67 = 3.3 + 0.032
is estimated the limit failure stress of the pipeline;
yield stress; t is pipeline’s wall thickness; D is pipeline’s outside diameter;L is
length of corrosion defect and d is depthof corrosion defect.Limit Failure
pressure is calculated as 32 MPa by the empirical formulaimproved ASME B13G,
which is close to the result of simulation and it means the finite element
method is a fitting way to predict the mechanical behaviors of transition
pipeline. But it’s too conservativeto predict the transition pipeline’s failure
pressure with corrosion defects inside and outside the pipeline at the same
time.It leads to energy and money wasting on the unnecessary repairs and
parts change. Elastic-plastic criterion is applied in this paper which is much
2.2 Numerical simulation model
The choice of pipeline’s material has great influence on the analysis of its
mechanical behaviors and failure pressure. The X65 pipeline is so widely
used in actual working conditions that it was exampled in the paper. Density is
7850kg/m ³ ,young’s modulus of steels material is 207GPa,Poisson’s ratio
equals 0.3, yield strength is 448 MPa. Considering the effect hardening
properties have on the pipeline’s failure stress is essential. Material of
transmission pipeline has well property of plastic deformation and distinct
yield point so the Ramberg-Osgood(R-O) model is usually used to describe the
relationship of stress and strain.The curve tells pipeline’s mechanical behavior
well when the strain is small,but it will have errors fitting the actual
stress-strain curve when the strain is big. So the improved R-O model is
applied in the research instead. Details of steel material are showed in Fig 1.
ig.1 stress-strain curve of X65
Based on the symmetry structure and load of transmission pipeline, a quarter
model is built. In order to simplify the calculation process, some assumptions
a. Only inner pressure applies on the inner face of pipeline.
b. Only pipeline’s section with corrosion defects is studied.
c. Other elements such as properties of buried soil and situation outside
the pipeline are not considered.
d. The corrosion pit is modeled to transit smoothly to contact area of
pipeline through the circular beads.
Fig.2 Finite element model
The model is meshed in a finite element method by advanced post-processing
software. Grids of the region around the corrosion defect is dividedmore
intensively to calculate more accurately. The geometry parameters oftransition
pipeline with corrosion defect inside is showed in Table1
able 1 The geometric parameters of pipeline and corrosion defect
3 Simulation results and discussion
When the defect’s length is 240 mm, width is 40 degrees, depth is 3mm, Von
Mises stress of pipeline distribution under different inner pressure is showed
in Fig.3. It can be seen that stress appears in the corrosion defects edge region
first and extends to the whole defect with the increasing inner pressure.
Compared with the circular stress changes, axial changes are more rapid and
have wide distribution. The maximum Von Mises stress increases with the
inner pressure and its location moves from edge of the corrosion defect to
thecenter section. Once the maximum pressure exceeds the limit pressure, the
distribution would increase rapidly generating the obvious deformation of
3.1 Effects of corrosion defects distributed axially
When inner and outer corrosion defects are aligned axially, the distance
between them is describe by letter with values of 0,0.5l, l and1.5l. l is half
length of single defectas 0.12m. Observed from distribution and curve in Fig.4,
Fig.5, Fig.6, maximum stress happens on the defects’ edges, increases then
expands to the defects’ center areas with increasing inner pressure. Stress on
the inner face is always larger than the outer face, close to each other since it
reaches the yield point. Different from the close stress when deformation
comes to the pipeline, stress impacting region is much wider in outer
corrosion defect. The maximum deformation will happen at outer corrosion
defect center area approaching inner corrosion defect.
Fig.3 Finite element model of corroded pipeline
Once defects have overlapping area, it will have a big influence on the stress of
pipeline. Stress will be affected by the inner pressure more easily and rise rate
is higher when the overlapping area is not the whole defect big. With the
decreasing distance between the two defects, not only the maximum Von
Mises stress is much higher, but also the strain change more rapidly under the
same inner pressure. Maximum stress appears on the defect inside initially,
then transits to the defect outside with the increasing inner pressure.
Fig.4 Max Von Mises stress (a=1.5l)
Fig.6 Max Von Mises stress (a=0.5l)
Fig.5 Max Von Mises stress (a=l)
Fig.7 Plastic strain of defects area
Fig.8 shows failure stress grows with increase of defects’ axial distance. Stress
is little different when a equals 0, 0.5l and l, 1.5l respective. Once the
superposition is not zero, inner stress increases rapidly to reach the yield
stress point and cause large deformation of corroded pipeline.
Fig.8 Failure pressure with different corrosion defects’ axial distances
3.2 Effects of corrosion defects distributed circumferentially
Circumferentially interactive defects can be researched by the circular angle
between inner defect andouter defect. The whole finite element model is
showed in Fig.9. The angle between inner and outer defect is 60 degrees.
ig.9 Finite element model of pipeline with corrosion defects
Fig.10 (a) is the curve of maximum Von Mises stress under increasing inner
pressure when βequals 60 degrees. Fig.10(b) is the curve of maximum Von
degrees.Maximum Von Mises stress changes with inner pressure, inner defect
and outer defect’s stresses are almost the same until it reached the yield stress.
maximum stress of outer defect will be bigger than the inner one with the
continually increasing inner pressure.
Fig.10 Max Von Mises stress curve of inner and outer corrosion defects
Fig.11 (a) is the Von Mises stress distribution of corrosion defects when β
equals 60 degrees while Fig.11 (b) shows it when β equals 50 degrees. As
stress displayed inFig.11 (a), maximum Von Mises stress always appears on
edge of defect firstly, then spread similar to it is single defect inside the
pipeline. Maximum stress of outer defect arises on the edge close to the inner
defect. The interaction of inner and outer defects was small before the limit
pressure, but functioned heavily when it exceeded the limit pressure and soon
caused the sharp submission in location. corresponding to the part outer
defect close to the inner defect.
ig.11 Stress distribution of defects area under different inner pressures
When β=60°,Plastic strain occurred when the inner pressure increase to 18
MPa, at the adjacent edges of inner and outer defects. It increased with the
increasing inner pressure. When the maximum Von Mises stress exceeded the
limit inner stress, apparent deformation would take place at the outer defect’s
defect approaching to the inner defect. When β=50°,Plastic strain occurred
when the inner pressure increase to 16 MPa. Fig.12 (b) displays similarly
except the large plastic appears strip shaped compared to the oval shaped in
Fig.12 (a). deformation happens in the outside corrosion defect of the pipeline.
Fig. 12 Plastic strain of defects area under different inner pressures
Inner corrosion defect’s margin and outer corrosion defect’s margin will be
tangent when βreduce to 40°, plastic strain distribution changes differently
with the overlapping area of inner and outer corrosion defects. Large
deformation lies in inner corrosion defect border, expand along the axial
direction faster than circular direction. Inside corrosion defect’s stress is
easier to reach the yield stress point than outside, but they have little
differences after the yield point. Once the two defects have overlapping
regions, it will have a great influence on the stress under higher inner
Fig.13 Max Von Mises stress of corroded pipeline under different inner pressures
Plastic strain is much bigger when β=30°, growth rate is much higher and
large deformation appears more rapidly with lower inner pressure. Plastic
strain appears exactly close to both long sides of inner and outer corrosion
defects firstly and distribute along the sides.
ig.14 Von Mises stress of defects area under different inner pressures
Fig.15 Plastic strain distribution of defects area
Coincident region will be just half corrosion defect since βdecreases from 20°.
Maximum Von Mises stress increases with the inner pressure before it reaches
yield stress point and after that it will keep stable range. It decreases with
decreasing degrees between inner and outer defects and it’s contrary to the
tendency when β is greater than 20°.
Fig.16 Maximum Von Mises stress curves of corroded pipeline
ig.17 Von Mises stress distribution of defects area
Maximum plastic strain appears at the edge of inner corrosion defect and on
the inner face only. Pipeline deformation spreads to the whole defect area with
increasing inner pressure, maximum plastic strain lies the inside corrosion
defect’s fillet and outside corrosion defect’s center. Plastic strain is nearly zero
under lower inner pressure when β equals 0° but rises at more rapid rate once
it emerges. Variation is similar when β is 20° and 10°.
Fig.18 Plastic strain distribution of defects area (β=20°,10°,0°)
Fig.18 shows the failure pressure of corroded pipeline with different corrosion
defect types based on the β’s value. Failure pressure increases with increasing
β generally as the interaction between inside and outside corrosion defects
becomes weaker. So do the safety and mechanical properties of corroded
Fig.19 Failure pressure with different corrosion defects’ circumferential locations
3.3 Effects of inner and outer layered corrosion defects
Practical situation is complex that corrosion defects is just the same of size.
For the defect is always irregular, it can be simplified through the relative size
with each other. Define the inner corrosion defect as the default model,
distinguish cases by the outer defect’s ratio of the inner one and study
mechanical behaviors transition pipeline. Outer corrosion defect’s size is half
of the inner oneWhen ratio is 0.5, same as the inner one as ratio is 1 and twice
the inner one as ratio is 2.
Fig.20 Von Mises stress distribution of corroded pipeline when ratio is 0.5
Fig.21 Von Mises stress distribution of corroded pipeline when ratio is 1
When ratio equals 1, the overlapping part is the whole corrosion defect.
Corroded section of pipeline can be regarded as thin-wall pipeline
approximately. Plastic strain certainly increase rapidly under lower inner
pressure and cause deformation easily. But when ratio doesn’t equal 1, surface
smaller-area corrosion defect lies has influence on the mechanical behaviors
of pipeline. Yield point is sooner to get when the outer defect is smaller the
inner one and plastic strain values larger than when the deformation appears.
Fig.22 The maximum Von Mises stress curves Fig.23
Fig.23 Plastic strain histogram
Fig.24 shows when ratio=0.5, maximumplastic strain appears on the edge of
outer corrosion defect outside the pipeline firstly, then transforms to the same
location inside the pipeline, concentrates the center region of the corrosion
defect outside. when ratio is 2, the maximum plastic strain occurs at the
circumferential edge of corrosion defect inside and finally transforms to the
center region of corrosion defect outside as well.
Fig.24 Plastic strain distribution of defects area under different inner pressures
Failure pressure of corroded pipeline is shown in Fig.25. Failure pressure
decreases with the ratio of corrosion defects decreases.
Fig.25 Failure pressure of corroded pipeline with different ratio
Both Von Mises stress and plastic strain increase with the increasing inner
pressure. Growth rate will be faster after stress exceeds yield point. Stress is
easy to increase when axial distance aand circular degree βdecrease.
The Maximum Von Mises stress and plastic strain appear on the long side of
the defect. Stress functioned area expands along the same direction of
pipeline with defects arrangements. The maximum deformation lies the center
area of outer corrosion defect close to the inner one and the exact center of
inner corrosion defect.
Once the two defects have overlapping area, plastic strain rising rate of
pipeline increases faster based on the rising area’s proportion, while its
mechanical and usage properties decreases.
This paper is supported by Project of State Key Laboratory for Strength and
Vibration of Mechanical Structures (SV2017-KF-08), Chengdu science and
technology plan (2016-HM01-00306-SF) and Science and Technology
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