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OMAE2005-67216

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Proceedings of OMAE2005
24th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2005)
June 12-17, 2005, Halkidiki, Greece
OMAE2005-67216
REELING EFFECT ON THE ULTIMATE STRENGTH OF SANDWICH PIPES
Xavier Castello
Ocean Engineering Department, COPPE/UFRJ
Rio de Janeiro, Brazil
xavier@lts.coppe.ufrj.br
ABSTRACT
Sandwich pipes composed of two steel layers separated by
a polypropylene annulus can be used for the transport of
oil&gas in deepwaters, combining high structural resistance
with thermal insulation in order to prevent blockage by paraffin
and hydrates.
In this work, sandwich pipes with typical inner diameters
of those employed in the offshore production are analyzed
numerically to evaluate the ultimate strength under external
pressure and longitudinal bending as well as the effect of the
reeling installation method on the collapse pressure.
Numerical models were developed using the commercial
finite element software ABAQUS. The validation was based on
experimental results. The analyses for combined loading were
performed using symmetry conditions and the pipe was reduced
to a ring with unitary length. The analysis of bending under a
rigid surface was simulated numerically according to the
experiments performed using a bending apparatus especially
built for full scale tests. Symmetry conditions were employed
in order to reduce the analysis to a quarter of a pipe. Mesh
sensitivity studies were performed to obtain an adequate mesh
refinement in both analyses. The collapse pressure was
simulated numerically either for the pre or post reeling process.
Bauschinger effect was included by using kinematic hardening
plasticity models. The influences of plasticity and out-ofroundness on the collapse pressure have been confirmed.
NOTATION
D
Dmin
Dmax
Dn
K
Kco
L
M
diameter
minimum diameter
maximum diameter
nominal diameter
curvature
collapse curvature
length
moment
Segen F. Estefen
Ocean Engineering Department, COPPE/UFRJ
Rio de Janeiro, Brazil
segen@lts.coppe.ufrj.br
P
Pd
Pco
Ri
Re
t
x, y, z
∆
ε
ε eqp
θ
σ
σ eq
pressure
design point
collapse pressure
internal radius
external radius
thickness
coordinate axes
ovalization
strain
equivalent plastic strain
rotation angle
stress
Von Mises equivalent stress
INTRODUCTION
New concepts of especial submarine pipes have been
proposed mainly to allow an adequate oil&gas transportation
flow. It is the case of both Pipe-In-Pipe (PIP) and Sandwich
Pipe (SP). PIP are composed of two concentrically mounted
steel pipes with the annular space filled with circulating hot
water or materials with pre-defined thermal insulation
properties. The objective of this type of pipe is to increase the
thermal insulation capacity to prevent blockage of the line
caused by dropping the fluid temperature to that required for
paraffin or hydrate formation. One of the advantages of PIP
system is the possibility of using materials with excellent
thermal properties, considering that the structural integrity is
provided independently by the outer and inner steel layers [1].
In the case of SP, object of this study, the annular layer
characteristics differ from PIP by satisfying simultaneously
mechanical and thermal requirements. Consequently, it is an
interesting option for ultra deepwaters under conditions which
require thermal insulation for flow assurance.
Numerical and experimental studies carried out by Estefen
et al. [2] for the limit strength, under combined external
1
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pressure and bending, indicate that SP are viable for application
in water depths up to 3000m. Inter-layer contact behavior, i.e.
the degree of adhesion, was observed to have significant
influence on the collapse pressure. Among the advantages
compared with single wall pipe, it was observed a substantial
higher bending capacity for equivalent external pressure, with
similar steel weight and less submerged weight. Structural
resistance is affected by the chosen material of the annular
layer. Polypropylene was adopted in the present work for
reasonably low cost, good mechanical properties and relatively
low thermal conductivity. Active heating system using
electrical wires, associated with passive insulation due to the
annular material was evaluated by Su Jian et al. [3, 4]. The
study of the heat transfer in transient flow for a deepwater
scenario indicates the necessity to input a certain amount of
heating to avoid line blockage in case of production
interruption or for long distance tieback.
In this work numerical modeling of the ultimate strength
was evaluated for combined external pressure and longitudinal
bending of the sandwich pipe with geometric properties (Table
1) similar to the prototypes to be fabricated by
TENARISCONFAB as part of a collaboration project with
COPPE/UFRJ to perform experimental tests at the Submarine
Technology Laboratory (LTS). Mesh refinement studies were
conducted to obtain the numerical model to be used to evaluate
the prototypes ultimate behavior. Symmetry conditions for halftransversal section and half-length were considered to minimize
the computational effort. Later, another model was developed
to study the residual effect of the reeling installation method
through numerical simulation of the process of bending and
rectification of pipes used at LTS. Symmetry of half-transversal
section and half-length in relation to the actual pipe length used
in the apparatus was adopted. Kinematic hardening plasticity
models were introduced to simulate the Bauschinger effect for
the metal layers. After the bending and rectification of the
sandwich pipe the collapse pressure was determined to verify
the influence of this process on the ultimate strength. Moreover,
the curves for moment-curvature and stress-strain are
determined to provide a better understanding of the pipe stress
and strain distributions.
SANDWICH PIPE MODEL FOR PRESSURE AND
BENDING ANALYSIS
The finite element program ABAQUS [5] was employed
for the structural analyzes. Another program written in
FORTRAN language was used initially to generate the mesh
with nodes and elements of the sandwich pipe with geometric
imperfection in the form of initial ovalization. For all models
symmetry conditions for half-transversal section and halflength were assumed.
Figure 1 shows an example of the model used for the
ultimate strength analysis. One solid element is considered in
length and for each metal layer and two solid elements for the
polymer layer.
The symmetry conditions applied to the X-Y and Y-Z
planes are the displacement node constraints in the respective
normal directions.
Table 1 presents the geometric properties of the analyzed
sandwich pipe. The steel pipes were selected according to API
5L standard. Geometry was determined based on
TENARISCONFAB pipe availability in stock and in
accordance with the LTS hyperbaric chamber capacity
(50MPa), considering that experimental tests are planned.
Figure 1: Finite element mesh for the sandwich pipe ring
Table 1: Geometrical properties of the analyzed sandwich pipe
Re (mm)
t (mm)
Dn (in)
Ri (mm)
6 5/8
77.75
84.15
6.4
Annular
84.15
103.15
19
8 5/8
103.15
109.55
6.4
Initial ovalization of 1% was adopted for the mesh
sensivity analyzes, which is calculated by the expression:
D
− Dmin
.
(1)
∆ 0 = max
Dmax + Dmin
Smaller diameter along the pipe length is coincident with
the bending plane to generate lower bound values
representative of the ultimate strength.
For both external pressure and bending simulation acting
separately Riks method and automatic increment control have
been employed, respectively. Combined loading was initially
implemented by fixed increments of external pressure followed
by incremental rotation until buckling failure has been
achieved. The external pressure is applied through surface load
on the external pipe. The bending was induced by the use of a
reference node located at x=L (model length), y=0 and z=0,
where the rotational displacement in z axis is applied.
Automatically generated kinematic coupling equations are used
to couple the degrees of freedom of the nodes of the transverse
plane to the reference node. It is assumed that this plane
remains flat and normal to the neutral line during the loading.
Additionally, the x degree of freedom coupling induces a plane
strain state for the section, which is needed for simulating a
long pipe.
The curvature applied to the pipe is calculated by the
following equation:
K =θ L ,
(2)
where the rotation angle θ (in radians) is input for each load
step.
The use of displacement control for the bending loads
allows extending the analysis even after the ultimate load, thus
generating the unloading moment-curvature relationship.
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However, in some cases the analysis ends just after reaching the
maximum moment because of excessive element distortion
leading to difficulties in obtaining the pipe ultimate strength.
The collapse curvature corresponds to the maximum moment
reaction at the reference node.
In all models the mesh was generated using threedimensional quadratic solid elements C3D27, with twentyseven nodes and three degrees of freedom per node. As the
polymer has volumetric incompressible characteristics,
elements with mixed formulation C3D27H were used in the
annular layers. Mixed formulation consists of calculating
element pressure stress independently of the displacement
stress to avoid that a small change in displacement produces
extremely large changes in pressure. This happens when
Poisson ratio reaches a value close to 0.5 or the bulk modulus is
much larger than the shear modulus.
MATERIAL MODELING
API X-60 steel was used for inner and outer pipes. The
proportional limit stress and yield stress are 310.38MPa and
481.46MPa, respectively. True stress versus logarithmic plastic
strain curve, shown in Figure 2, was obtained by tensile tests as
well as the derived elastic modulus (E) of 206,863MPa and
Poisson ratio (ν) of 0.3.
800
True Stress (MPa)
700
600
dε
p
=
where: H =
9 1 Sdσ
S,
2
4 H σ eq
dσ 11
dε 11p
or H =
(4)
dσ 11
−E.
dε 11
The notation indicates x direction for the uniaxial case.
The dependency of the stress on the strain is simulated for
the entire elastic-plastic regime and the material non-linear
effects are considered.
For the simulation of the reeling process a kinematic
hardening plasticity model is added to the isotropic model, so
that the Bauschinger effect can be simulated during the cyclic
loading for more accurate results. The Bauschinger effect is
characterized by a reduced yield stress under reverse loading
after plastic deformations have occurred in the initial loading.
This phenomenon tends to reduce its influence as the cycles
progress. However, in the present simulation only one cycle
and a half is performed, therefore it is not necessary to analyze
the effects for stabilized cycles.
Similar to the previous plasticity model, the subsequent
yielding surface is represented by:
1
⎛3
⎞ 2
(5)
f (σ − α ) = ⎜ (S − a )(S − a )⎟ = σ eq ,
⎝2
⎠
where α is the actual position of the yielding surface and a is
the center of the surface in the deviatoric stress space. Now, the
center of the surface translates in the direction of the plastic
deformation increment. Figure 4 shows the representation of
the movement of the yielding surface.
500
σ1
400
300
Initial yielding surface
200
Subsequent y. s.
100
0
0
0.025
0.05
0.075
0.1
0.125 0.15
0.175
0.2
σ2
Logarithmic Plastic Strain
Figure 2: True stress-logarithmic plastic strain curve
API X-60 steel
Figure 3: Representation of the initial and subsequent
yielding surfaces of the J2 flow rule theory for isotropic
hardening in the stress space
The steel layers are modeled by plasticity theory of
potential flow rule J2 associated with isotropic hardening and
Von Mises yielding criteria for the combined loading models.
Summarizing, the initial yielding surface represented in the
stress space in Figure 3, changes only in size, which is defined
by the yielding surface expression with radius equal to Von
Mises equivalent stress calculated at the last increment as a
function of the stress state. The yielding surface expression is
given by:
⎛3
⎞
f (J 2 ) = ⎜ S ij S ij ⎟
⎝2
⎠
where
1
2
= σ eq ,
σ1
Initial yielding surface
Subsequent y. s.
σ2
(3)
S ij is the deviatoric stress tensor.
Figure 4: Representation of the initial and subsequent
yielding surfaces of the J2 flow rule theory for kinematic
hardening in the stress space
The incremental plastic strains are obtained solving the
flow rule as a function of the local hardening module (H) and
the stress state σ , resulting in the Prandtl-Reuss expression:
3
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In the non-linear kinematic hardening model, the evolution
law of the yielding surface consists of a component of
kinematic hardening, which describes the translation of the
surface in the stress space by the variable α . This component
is defined by the combination of a pure kinematic term
(Ziegler’s linear hardening law) and a relaxation term, which
introduces the non-linearity. The law is expressed by:
1
(6)
dα = C
(σ − α )dε eqp − γ α dε eqp ,
σ eq
where C and γ are material parameters adjusted by cyclic tests,
C is the initial kinematic hardening modulus and γ determines
C variation rate.
The finite element program provides an option to include
the kinematic hardening and Bauschinger effect consequently,
through a uniaxial tensile test, being only recommended when a
few cycles will be performed.
Solid polypropylene was modeled as non-linear elastic
material (hyperelastic) and volumetrically incompressible. A
stress-strain curve is used by the program to obtain an Ogden
approximation adjust, where the strain energy is given by the
expression:
N
U =
∑
i =1
2 µ ⎛ αi
αi
αi
⎜ λ1 + λ2 + λ3 − 3 ⎞⎟ +
⎠
α i2 ⎝
∑ D (J
N
1
i =1
el
)
−1
2i
,
(7)
i
where N, µi, αi and Di are material parameters.
−1
The deviatoric strains are given by λi = J 3 λi , where λi are
the components of the principal strain. J parameter is the ratio
of total volume variation, J = dV dV0 , where V and V0 are the
final and initial volumes, respectively. Jel is the ratio of elastic
volume variation given by J el = J J th . For the case where no
thermal strains occur ( J th = 1 ), we get J el = J .
Shear stress and compressibility modules (bulk modulus) are
given by µ 0 =
N
∑µ
i =1
i
and K =
2
, respectively.
D1
The parameters are defined by uniaxial tensile and
compressive tests. Approximate results are obtained only for
uniaxial tensile test. The Di parameter is obtained by volumetric
compression test.
Utilizing N equal to 2 and informing the uniaxial stressstrain curve of polypropylene for ambient temperature, Figure
5, the parameters are obtained by the automatic adjust of the
finite element program, as below:
µ1 = -769.66
µ2 = 944.98
α1 = 17.68
α 2 = 15.42
D1 = 0
D2 = 0
MESH SENSIVITY
The same numerical model employed in previous works
[2] has been validated with experimental tests of small-scale
specimens and a parametric study indicated possible geometries
for offshore application which are similar to those here
analyzed. Mesh sensivity has also been considered. The
intention now is to prepare a numerical model for further
experimental
correlation
with
full-scale
prototypes
(COPPE/UFRJ-TENARISCONFAB collaboration project). The
present work includes a mesh sensivity analysis for a pipe with
length equal to that adopted for tests at the LTS bending
apparatus.
The half ring presented earlier is first modeled with 10, 16,
20 and 24 elements in the circumferential direction for 5, 6.4,
10 and 20mm longitudinal length. It is well known that during
the collapse of pipes by external pressure shell bending in the
circunferencial direction occurs caused by the ovalization
increase and, therefore, the mesh should be refined
circumferentially. The results for collapse pressure (Pco) with
1% of initial ovalization are presented in Table 2, where Nc is
the number of elements in the circunferencial direction and the
deviation is relative to the Pco obtained for the long pipe (Table
3), taken as reference after Nc is selected.
Table 2: Sandwich pipe ring mesh refinement results for
external pressure collapse
L (mm)
Nc
Pco (MPa) Deviation (%)
10
45.05
-1.12
16
44.4
0.34
10
20
44.3
0.56
24
44.25
0.67
10
45.15
-1.35
16
44.5
0.11
6.4
20
44.4
0.34
24
44.35
0.45
10
45.25
-1.57
16
44.5
0.11
5
20
44.4
0.34
24
44.4
0.34
Figure 5: Adjusted uniaxial stress-strain curve for
polypropylene
4
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Colapse Pressure, Pco (MPa)
46
45.5
45
44.5
44
43.5
5
10
15
20
25
30
Nc
L = 5mm
L = 6.4mm
L = 10mm
Figure 6: Collapse pressure results for sandwich pipe
ring mesh refinement
Figure 6 indicates that values of Pco tend to converge for
Nc greater than 20. It is also observed that the ring lengths (L)
5 and 6.4mm converged with a deviation of 0.34%.
In order to analyze a numerical model to evaluate a more
precise Pco (used as reference in Table 2) a sandwich pipe is
modeled with the same length as that of reeling simulation
apparatus. Half-length (2600mm) and half-transversal section
are considered and the pipe end is radially constrained, Figure
7. The ovalization is uniform for all pipe length and equal to
1% as before. Nc is assumed as 20 and the element length L is
refined according to Table 3, where Nl is the number of
elements in the longitudinal direction.
The collapse pressure was practically not influenced by the
length variation. Computer time increases too much for Nl
greater than 65, without benefit for Pco accuracy.
The 40mm element length was adopted to obtain Pco
reference in previous sandwich pipe ring mesh refinement
(Table 2). The 65mm element length was not adopted because
the next simulation (reeling) uses contact elements and the
analysis does not converge with coarse longitudinal mesh.
Table 3: Collapse pressure results for long sandwich pipe using
longitudinal mesh refinement
L (mm)
Nl
Pco (MPa)
65
40
44.45
40
65
44.55
20
130
44.55
10
260
44.55
6.4
406
44.55
5.2
499
44.6
Figure 8: Collapse curvature for the long sandwich pipe
Ring meshes for collapse curvature results were evaluated
for the same three cases (5, 6.4 and 10mm length) and
compared with the result for the long pipe, Figure 8. Table 4
shows the results, where the first line is related to the long pipe
(with 65 elements in longitudinal direction and 2600mm
length), with collapse curvature value taken as reference for
deviation calculation.
Table 4: Collapse curvature results for different sandwich pipe
ring lengths compared to the long pipe
L (mm) Kco (1/m) Deviation (%)
1.119
40
1.168
4.38
10
1.121
-0.18
6.4
1.103
1.43
5
It can be noted that the 6.4mm element length is adequate
for further analyzes. Moreover, the 6.4mm ring length
generates a deviation of only 0.34% for collapse pressure
(Table 2) against 0.56% for the 10mm ring length.
LIMIT STRENGTH CURVES FOR SANDWICH PIPE
The numerical ring model with 20 circumferential
elements and 6.4mm length has been employed to generate the
ultimate strength curve of the sandwich pipe under combined
external pressure and longitudinal bending. Sandwich pipe
geometries are indicated in Table 1. Initial ovalization of 0.2%
was adopted. Figure 9 shows the ultimate strength curve under
combined external pressure and bending. The design point Pd
indicates approximately the values of pressure and curvature
acting on the pipe during the installation process for 3,500m
water depth. Figure 10 presents the moment-curvature curves
for different initial applied pressure given as a percentage of the
collapse pressure.
Figure 7: Long sandwich pipe with longitudinal
mesh refinement
5
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51
Collapse Pressure, Pco (MPa)
60
Pressure, P (MPa)
50
40
Pd
30
20
10
0
0
0.2
0.4
0.6
0.8
1
50
49
48
47
46
45
1.2
44
Curvature, K (1/m)
0
Figure 9: Ultimate strength under pressure and bending
0.2
0.4
0.6
0.8
1
1.2
Ovalization (%)
Figure 11: Influence of the initial ovalization on the collapse
pressure of the sandwich pipe
300000
Moment, M (N.m)
250000
These results show the importance of having a good
fabrication control and also that the pipe must be stored and
installed appropriately to avoid excessive out-of-roundness.
200000
150000
APPARATUS FOR EXPERIMENTAL SIMULATION OF
THE REELING INSTALATION PROCESS
100000
50000
0
0
0.2
0.4
0.6
0.8
1
1.2
Curvature, K (1/m )
0%Pco
20%Pco
40%Pco
60%Pco
80%Pco
The apparatus for the simulation of the reeling process
allows the pipe to undergo different longitudinal deformations
when reeled on a cylindrical surface, reeled-off and rectified
using reverse bending. Figures 12 and 13 shows a schematic
view of the reel-on and the subsequent reel-off process on a
typical reel-lay ship, as indicated in Figure 14.
Figure 10: Moment-curvature curves for different initial
pressure acting on the sandwich pipe
Each point representing the combined load for ultimate
strength in Figure 9 is related to the maximum moment for each
initially prescribed pressure (0, 20, 40, 60, 80% of collapse
pressure) in Figure 10.
The design point (Pd) is calculated adopting a 1.33 safety
factor over the collapse pressure and a maximum longitudinal
strain according to API of 0.5%. Expression (8) relates
curvature K and longitudinal deformation ε:
ε = KRe
(8)
INFLUENCE OF THE
COLLAPSE PRESSURE
OVALIZATION
ON
Figure 12: Reel-on process, bending
THE
The same mesh from the previous analyzes has been also
employed to evaluate the influence of different magnitudes of
initial ovalization (0.1, 0.2, 0.5 and 1%) on the collapse
pressure. The results presented in Figure 11 indicate a reduction
of 12.1% in collapse pressure for an ovalization increase from
0.1 to 1%.
Figure 13: Reel-off process, unbending/rectification
6
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Figure 16: Extended actuators (bending)
Figure 14: Typical reel-lay ship [6]
The load history (moment-curvature curve) experienced by
a given section during the whole installation process is shown
in Figure 15, according to stages 1 to 5 indicated in Figures 12
and 13.
Figure 17: Retracted actuators (rectification)
REELING PROCESS SIMULATION MODEL
Figure 15: Moment-curvature loading history
during the reeling process [6]
As the maximum curvature imposed on a pipe occurs in the
first stage (1-2), and no plastic deformation is induced in the
intermediary cycle 2-3-4, the laboratory test is carried out for
stages 1-2-3-5-1. Thus, in order to simplify the test without
affecting the final result, the load stage 3-4 (bending on the
aligner) is not reproduced by the apparatus.
The pipe is placed between the bending formers, which are
connected by hydraulically operated rods, forming a single
piece that involves the pipe. Pipe ends react against rollers,
allowing it to rotate and slide longitudinally, but preventing it
from moving transversally. In these experiments, the curvature
radii of bending and rectification formers are 6 and 30 meters,
respectively. Figures 16 and 17 show the final movement
positions of the formers when the hydraulic actuator is
extended and retracted, respectively.
The reeling installation process was originally simulated
for single wall pipe and the results compared with those from
full scale tests [7]. In this paper the model was adapted to three
layer sandwich pipe.
It was necessary to model the sandwich pipe with the same
length as used in the bending apparatus to make it possible to
analyze the complete stress-strain and moment-curvature
curves for the whole process.
Half-length and half-transverse section symmetry
conditions were considered, Figure 18. Table 1 indicates the
pipe geometric properties used in the analysis. Initial
ovalization of 0.2% is adopted. Half-lengths of analyzed pipe
and formers are 2600mm and 2000mm, respectively.
Figure 18: Step 0 – Undeformed configuration
The model was implemented with C3D27 elements, the
same employed in previous limit strength analyzes. Kinematic
hardening plasticity model was used in addition to the isotropic
7
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model, as explained earlier, to simulate the Bauschinger effect
for the steel layers.
The bending and rectification formers were modeled
through analytical surfaces. On the external pipe contact
surfaces were generated to simulate the interaction forces.
The curvature was induced by applying displacement at the
pipe end and keeping the bending formers fixed. Reference
nodes coupled with nodes on the section plane were used both
at the pipe end and on the half-length symmetry section.
Displacement in y direction was applied at the pipe end to
induce pipe curvature on the formers. On pipe mid-section
(x=0), restrictions associated with the symmetry condition were
applied to the reference node, which were then transferred to
nodes on the transverse section. Reaction moment around axis z
could then be monitored and the moment-curvature curve
plotted for the pipe mid-section. Curvatures were obtained by
the rotation angle of the reference node at the pipe end.
Complete bending, rectification and elastic spring-back
process (stages 1-2-3-5-1) was modeled through four load
steps, with external pressure applied after the rectification, as
shown below:
1) Displacement of the pipe end from the initial position
(step 0) to the bending former;
2) Reverse displacement to the rectification former;
3) Displacement of the rectification former away from
the pipe;
4) Increments of external pressure applied up to the
collapse failure.
All the mentioned displacements are applied along the y
axis. Figures 19, 20 and 21 show the deformed configurations
according to the load steps. Single line pipe indicated in the
figures represents the pipe undeformed configuration.
Figure 21: Step 3 - Displacement of the rectification former
away from the pipe
Results of the collapse pressure of the pipe before and after
the reeling process were obtained. The results of the maximum
equivalent plastic strain and stress for each load step are
presented in Table 5.
Table 5: Results for reeling installation process,
load steps 1 to 3
Variable
Step 1 Step 2 Step 3
ε eqp (10-2)
2.149
4.076
4.076
σ eq (MPa)
487.6
449.8
311.5
∆ (%)
0.85
0.62
0.56
It can be seen that in the steps 1 and 2 the stresses
remained high and only decreased after the pipe was released
(step 3), when a residual stress of 311.5MPa was recorded.
Equivalent plastic strain reached its highest value during the
second load step.
At step 4 the collapse due to external pressure occurred
under 47.58 MPa compared with 48.24 MPa before the reeling
simulation. It represents a collapse pressure reduction of only
1.4%, despite an ovalization increase from 0.2% to 0.56%.
Symmetrical distribution of the equivalent plastic deformations
accumulated after the reeling process is shown in Figure 22.
y
x
Figure 19: Step 1 – Displacement of the pipe end
over the bending former
Figure 22: Distribution of the equivalent plastic
strains at the end of step 4
Figure 20: Step 2 – Reverse displacement of the pipe end
over the rectification former
The pipe deformed configuration under external pressure
with collapse failure initiation at the pipe mid-section is shown
in Figure 23.
8
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Residual longitudinal stress of 89.55MPa and strain of
0.13% were observed in the outer pipe (larger cycle) in Figure
25. The inner pipe has only a small strain value, with residual
stress close to zero.
CONCLUSIONS
Figure 23: Pipe deformed configuration at collapse pressure
Figure 24: Moment-curvature for steps 0-1-2-3 of the bending
and rectification process for the sandwich pipe
Figure 25: Longitudinal stress-strain curves for the
radially-outermost upper points of the steel pipes
The reverse moment attains its maximum during step 2,
when the pipe is back to its initial position (reel-off) and starts
to be rectified, Figure 24. At the end of the process the pipe is
released (step 3). In addition, a final curvature close to zero is
obtained, which suggests that rectification of the residual
curvature was successfully performed.
It can be seen that the moment values necessary to induce
and reverse pipe are different, due to the use of kinematic
hardening plasticity models to include the Bauschinger effect.
Sandwich pipe suitable for 3,500 meters water depth
application was analyzed for limit strength under external
pressure and bending. In addition, the effects of the reeling
installation method on the collapse pressure were also
evaluated.
Two different numerical models were employed in the
computer simulations, full length pipe and ring section. For
ultimate strength analyzes of external pressure combined with
longitudinal bending the ring section was employed. The
reeling installation process, i.e. bending over a rigid surface and
rectification through reverse bending were simulated using
longitudinal symmetry for the pipe full length. Afterwards, the
sandwich pipe was submitted to increments of external pressure
up to the collapse failure.
Some of the main conclusions are outlined below:
¾ Based on the limit strength curve it was possible to
estimate a 3,500m water depth application considering
a realistic initial ovalization of 0.2%, 1.33 safety factor
for the external pressure and maximum longitudinal
strain during installation limited by API yield strain;
¾ The ovalization increase from 0.1 to 1% implied in
collapse pressure reduction by 12%;
¾ The collapse pressure obtained for the sandwich pipe
after the reeling process has not been significantly
reduced (1.4%) if compared with the pipe collapse
capacity before reeling, despite ovalization increase
from 0.2% to 0.56%;
¾ Reeling simulation indicates significant residual
equivalent strains of 4.08%, although the longitudinal
strain of 0.13% is still in the elastic range;
¾ The reverse moment for the pipe curvature
rectification is, approximately, 87.5% of the moment
to bend initially the pipe over the reel, confirming the
influence of the kinematic hardening plasticity model
which incorporates the Bauschinger effect;
¾ The maximum equivalent stress of 487.6MPa
measured during the reeling simulation is slightly
higher than the yield stress for the X-60 steel assumed
for the metal layer.
The results presented in this paper are associated with a
research work in progress about the offshore installation and
operation of sandwich pipes. Although the results so far
achieved have attended the initial expectations, further
experimental and numerical studies for full scale prototypes
have been planned to build up the necessary confidence for the
use of sandwich pipes in ultra deepwaters.
ACKNOWLEDGMENTS
The authors would like to acknowledge the Brazilian
Ministry of Education / CAPES for the financial support to the
first author and TENARISCONFAB for the help during the
definition of the prototype geometric properties.
9
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