Finite element model predicts local
conditions
With ultra deepwater pipelines being considered for water depths of nearly
3,000 m, pipe collapse, in many instances, will govern design. For example,
bending loads imposed on the pipeline near
the seabed (sagbend region) during installation will reduce the external
pressure resistance of the pipeline, and this design case will influence (and generally
govern) the final selection of an appropriate pipeline wall thickness.
To date, the deepest operating pipelines have been laid using the J-lay method, where
the pipeline departs the lay vessel in a nearvertical
orientation, and the only bending condition resulting from installation is near
the touchdown point in the sagbend. More recently, however, the S-lay method is
being considered for installation of pipelines to
water depths of nearly 2,800 m. During deepwater S-lay, the pipeline originates in a horizontal orientation, bends
around a stinger located at the stern or bow of the vessel, and then departs
the lay vessel in a near-vertical orientation. During S-lay, the installed pipe
experiences bending around the stinger (overbend region), followed by combined
bending and external pressure in the sagbend region.
In light of these bending and external
pressure-loading conditions, analytical work was performed to better understand
the local buckling behavior of thick-walled line pipe due to
bending, and the influence of bending on pipecollapse.
Variables considered in the analytical evaluations include pipe material
properties, geometric properties, pipe thermal treatment, the definition of
critical strain, and imperfections such as ovality and girth weld offset.
Design considerations
As the offshore industry engages in deeper water pipeline installations, design limits associated with
localbuckling must be considered and adequately addressed.
Instances of local buckling include excessive bending resulting in axial
compressive local buckling, excessive external pressure resulting in hoop
compressive localbuckling, or combinations of axial and hoop loading creating
either local buckling states. In particular, deepwater pipe
installation presents perhaps the greatest risk of local buckling, and a thorough understanding of these limiting
states and loading combinations must be gained in order to properly address
installation design issues.
Initial bending in the overbend may
result in stress concentrations in pipe-to-pipe weld offsets or in
pipe-to-buckle arrestor interfaces. Initial overbend strains, if large enough,
may also give rise to increases in pipe ovalization, perhaps reducing its collapse strength when installed at depth. Active bending
strains in the sagbend will also reduce pipe collapse strength, as has been previously demonstrated
experimentally.
Overall modeling approach
In an attempt to better understand pipe
behavior and capacities under the various installation loading conditions, the
development and validation of an all-inclusive finite element model was performed
to address the local buckling limit states of concern during deepwater pipe
installation. The model can accurately predict pipe local buckling due to bending, due to external pressure, and to
predict the influence of initial permanent bending deformations on pipe collapse. Although model validation is currently being
performed for the case of active bending and external pressure (sagbend), no
data has been provided for this case.
The finite element model developed
includes non-linear material and geometry effects that are required to
accurately predict buckling limit states. Analysis input files were
generated using our proprietary parametric generator for pipe type models that
allows for variation of pipe geometry (including imperfections), material
properties, mesh densities, boundary conditions and applied loads.
A shell type element was selected for
the model due to increased numerical efficiency with sufficient accuracy to
predict global responses. The Abaqus S4R element is a fournode, stress/displacement
shell element with large-displacement and reduced integration capabilities.
All material properties were modeled
using a conventional plasticity model (von Mises) with isotropic hardening.
Material stress-strain data was characterized by fitting experimental, uniaxial
test results to the Ramberg-Osgood equation.
Pipe ovalizations were also introduced
into all models to simulate actual diameter imperfections, and to provide a
trigger for buckling failure mode. This was done during model
generation by pre-defining ovalities at various locations in the pipe model.
Bending case
A pipe bend portion of the model was
developed to investigate local buckling under
pure moment loading. Due to the symmetry in the geometry and loading
conditions, only one half of the pipe was modeled, in order to reduce the
required computational effort. The pipe mesh was categorized into four regions
* Two refined mesh areas located over a
length of one pipe diameter on each side of the mid-point of the pipe to
improve the solution convergence (location of elevated bending strains and
subsequent buckle formation)
* Two coarse mesh areas at each end to
reduce computational effort.
Clamped-end boundaries were imposed on
each end of the pipe model to simulate actual test conditions (fully welded,
thick end plate). Under these assumptions, the end planes (nodes on the face)
of both ends of the pipe were constrained to remain plane during bending.
Loading was applied by controlled rotation of the pipe ends.
In terms of material properties, the
axial compressive stress-strain response tends to be different from the axial
tensile behavior for UOE pipeline steels. To accurately capture this difference
under bending conditions, the upper (compressive) and lower (tension) halves of
the pipe were modeled with separate axial material properties (derived from
independent axial tension and compression coupon tests).
In general, the local compressive
strains along the outer length of a pipe undergoing bending will not be uniform
due to formation of a buckle profile. In order to specify the critical value at
maximum moment for an average strain, four methods were selected based on
available model data and equivalence to existing experimental methods.
Collapse case
The same model developed for the bending
case was used to predict critical buckling under
external hydrostatic pressure. This included the use of shell type elements and
the same mesh configuration. In the analyses, a uniform external pressure load
was incrementally applied to all exterior shell element faces. Radially
constrained boundary conditions were also imposed on the nodes at each end of
the pipe to simulate actual test conditions (plug at each end). In contrast to
the pipe bend analysis, only a single stressstrain curve (based on compressive
hoop coupon data) was used to model the material behavior of the entire pipe.
The pipe bend finite element model was
validated using full-scale and materials data obtained from the Blue Stream
test program, both for "as received" (AR) and "heat
treated" (HT) pipe samples. Geometrical parameters were taken from the
Blue Stream test specimens and used in the model validation runs. Initial
ovalities based on average and maximum measurements were also assigned to the
model. The data distribution reflects the relative variation in ovality
measured along the length of the Blue Stream test specimens.
Axial tension and compression
engineering stress-strain data used in the model validation were based on
curves fit to experimental coupon test results. As pointed out previously,
separate compression and tension curves were assigned to the upper and lower
pipe sections, respectively, in order to improve model accuracy.
In the validation process, a number of
analyses were performed to simulate the Blue Stream test results (base case
analyses), and to investigate the effects of average strain definition, gauge
length, and pipe geometry. These analyses, comparisons and results were:
* The progressive deformation during
pipe bending for the AR pipe bend showed the development of plastic strain
localization at the center of the specimen
* A comparison between the resulting
local and average axial strain distributions for two nominal strain levels
indicated that at the lower strain level the distribution of local strain is
relatively uniform, at the critical value (peak moment) a strain gradient is
observed over the length of the specimen with localization occurring in the
middle, the end effects are quite small due to specimen constraint and were
observed at both strain levels
* The resulting moment-strain response
for the AR pipe base case analysis found the calculated critical (axial) strain
slightly higher than that determined from the Blue Stream experiments
* The effect of chosen strain definition
and gauge length on the critical bending strain for the AR pipe base case
analysis, using the four methods for calculating average strain, gave similar
results
* The critical strain value is somewhat
sensitive to gauge length for a variety of OD/t ratios
* The finite element results are seen to
compare favorably with existing analytical solutions and available experimental
data taken from the literature. For pipe under bending, heat treatment results
in only a slight increase in critical bending strain capacity.
Similar to the pipe bending analysis,
the plain pipe collapse model was also validated using full-scale and
materials data obtained from the Blue Stream test program, both for "as
received" (AR) and "heat treated" (HT) pipe samples. Pipe
geometry and ovalities measurements taken from the Blue Stream collapse specimens were used in the validation analyses.
Initial ovalities based on average and maximum measurements were also assigned
to the model at different reference points. Hoop compression stress-strain data
was used in the model, and was based on the average of best fit curves from
both ID and OD coupon specimens, respectively. To validate the pipe collapse model, comparison was made to full-scale results
from the Blue Stream test program which demonstrated a very good correlation
between the model predictions and the experimental results.
In addition to the base case, further
analyses were run for a number of alternate OD/t ratios ranging from 15 to 35. Similar
to the pipe bend validation, the OD/t ratio was adjusted by altering the
assumed wall thickness of the pipe. The finite element results have compared
favorably with available experimental data taken from the literature.
The beneficial effect of pipe heat
treatment for collapse has resulted in a significant increase in
critical pressure (at least 10% for an OD/t ratio of 15). The greatest benefit,
however, is observed only at lower OD/t ratios (thick-wall pipe). This can be
attributed to the dominance of plastic behaviour in the buckling response as the wall thickness increases (for a
fixed diameter). At higher OD/t ratios, buckling is
elastic and unaffected by changes in material yield strength.
Pre-bent effect on collapse
Finite element analyses were also
performed to simulate recent collapse tests
conducted on pre-bent and straight UOE pipe samples for both "as
received" (AR) and "heat treated" (HT) conditions. The intent of
these tests was to demonstrate that there was no detrimental effect on collapse capacity due to imposed bending as a result of
the overbend process. In the pre-bend pipe tests, specimens were bent up to a
nominal strain value of 1%, unloaded, then collapse tested
under external pressure only.
To address this loading case, a simplified
modeling approach was used whereby the increased ovalities and modified
stressstrain properties in hoop compression due to the pre-bend were input
directly into the existing plain pipe collapse model
(the physical curvature in the pipe was ignored).
A comparison between the predicted and
experimental collapse pressures for both pre-bent and straight AR and
HT pipes indicates that the model does a reasonable job of predicting the collapse pressure for both pipe conditions. It is also
clear that the effect of moderate pre-bend (1%) on critical collapse pressure is relatively small.
While the pre-bend cycle results in an
increased ovality in the pipe, this detrimental effect is offset by a
corresponding strengthening due to strain hardening. As a result, the net
effect on collapse is relatively small. For the AR pipe samples,
there was a slight increase in collapse pressure
when the pipe was pre-bent. Conversely, for the HT pipe, the opposite trend was
observed. This latter decrease in collapse pressure
can be attributed to two effects: the larger ovality that resulted from the
pre-bend cycle and the limited strengthening capacity available in the HT pipe
(the HT pipe thermal treatment increased the hoop compressive strength,
offering less availability for cold working increases due to the pre-bend).
Similar to previous experimental studies
on thermally aged UOE pipe, the beneficial effect of heat treatment was
demonstrated in the pre-bend analysis. The collapse pressure
for the pre-bent heat treated (HT) pipe is approximately 8-9% higher than that
for the as received (AR) pipe, based on both the analytical and experimental
results. This increase, however, is lower than that observed for un-bent pipe
(approximately 15-20% based on analysis and experiments).
This unique case of an initial permanent
bend demonstrated that the influence on the collapse strength
of apipeline was minimal resulting from an increase in hoop
compressive strength (increasing collapse strength),
and an increase in ovality (reducing collapse strength).
This directly suggests that excessive bending in the overbend will not
significantly influence collapse strength.
Future work includes advancing the model
validation to the case of active bending while under external pressure. This
condition exists at the sagbend region of a pipeline during
pipelay and, in many cases, will govern overall pipeline wall thickness design.
sumber : DeGeer, D. "Understanding Pipeline Buckling in Deepwater Applications". 27 Januari 2014. http://search.proquest.com/docview/227334397?accountid=31562
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