Proceedings of the ASME 2022 41st International
Conference on Ocean, Offshore and Arctic Engineering
OMAE2022
June 5-10, 2022, Hamburg, Germany
PIPELINE REEL-LAY FE SIMULATION: AN ADVANCED MATERIAL MODEL
CALIBRATED FROM TESTING
Chen SHEN
Richard STABLEFORD
Eric GIRY
Saipem SA
Saipem SA
Saipem SA
Montigny-Le-Bretonneux,
France
Montigny-Le-Bretonneux,
France
Montigny-Le-Bretonneux,
France
ABSTRACT
For small to medium size rigid pipelines, reel-laying is an
efficient installation method. Higher lay rates are achieved
thanks to unreeling rigid pipeline down to seabed. However, the
process is mechanically onerous. Pipelines go through
successive large bending strains up to 2% or 3%. This is the
primary degradation mechanism and affects the mechanical inservice performance of the subsea line. Assessment of material
response to the installation sequence is a key point for pipeline
engineering. Conventional monotonic material stress-strain
relation or cyclic Ramberg-Osgood models are not suitable for
repeated large bending sequences or reel-lay installation FE
simulations. A parameter-based material model has been
tailored for carbon steel seamless pipe under reeling. The
evolution of the material behaviour from the first load to
stabilised cycle is addressed, by introducing an Abaqus User
Subroutine written in FORTRAN. The material properties are
programmed in each straining cycle, then active in their
corresponding loading cycle. Specimens from DNV450 grades
pipe have been tested in an extensive small-scale test and
bending trial campaign in order to calibrate finite element
model. DIC is used during tensile test and LCF (Low Cycle
Fatigue) test to allow accurate measurement on large straining
ranges. The parameter-based model can provide response to the
first load, including Lüders plateau, up to stabilized hysteresis
loop; it is fully parametric by Python. Comparison is made with
the more conventional material model or full-scale bending
trials demonstrating improved accuracy and agreement with
testing. The proposed material model is part of an in-house
material model library integrated in a numerical tool package
dedicated to rigid pipeline design.
Keywords: Reeling, FEM, Parameter-based Material Model,
Abaqus Combined Hardening Model, Abaqus User Subroutine
NOMENCLATURE
DIC
DNVGL
DOF
DP3
EN
FEA
ISO
LCF
OD
PLET
ROV
SMLS
UKAS
UMAT
USDFLD
3-D
V003T04A024-1
Digital Imaging Correlation
Det Norse Veritas and Germanisher Loyd
Degree Of Freedom
Dynamic Positioning class 3
Europäische Norm
Finite Element Analysis
International Standards Organisation
Low Cycle Fatigue
Outer diameter of pipe
Pipeline End Termination
Remote Operating Vehicle
Seamless (pipes)
United Kingdom Accreditation Society
User-defined MATerial in Abaqus
USer-Defined FieLD in Abaqus
3 Dimensional
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OMAE2022-79856
1
INTRODUCTION
The Saipem Constellation is a recent reel-lay vessel which
in addition to heavy lift and extensive field development
equipment (DP3, ROV spread, large moonpool, enhanced PLET
handling capacity) has a rigid pipelay system capable of
installing reeled pipe up to 16” diameter in 4,000 m water depth
(FIGURE 1). The Saipem Constellation has a previous trackrecord for reeled pipelines but since taking ownership, Saipem
has expended extensive labour not only in generating onshore
stalk assembly and spooling facilities but also producing and
validating numerical computational models of the reeling
process.
A specific material model is needed. It should have the
ability to mirror the shape of the stress-strain curve through
multiple cycles and to assign the parameters to the material point
according to its loading cycle. Also, it shall be simple to calibrate
for project use and to avoid complicated User Subroutine such
as UMAT.
In this paper, a parameter-based material model is presented.
Based on Abaqus build-in combined isotropic/non-linear
kinematic hardening model, the proposed material model uses
Abaqus User Subroutines USDFLD and UHARD to enable
Abaqus to change the stress-strain relations and yield surface
evolution from the first load curve to the stabilised hysteresis
loop varying the material hardening property at each cycle.
FIGURE 1: SAIPEM CONSTELLATION REEL-LAY VESSEL
The pipeline is reeled, unreeled and straightened during
installation. Part of the pipe cross-section has experienced
varying levels of plastic deformation in compression and tension
over repeated cycles. The material plastic behaviour is modified,
often hardened, though the cycles for some parts of the pipe,
while some parts remain in the elastic domain [12][16]. Various
material models have been proposed to take into account the load
history so that the response varies over cyclic loadings. For
subsea flowlines, ovality is the main response to be checked
either to meet standard requirements [2][7][8], to anticipate
failure mode such as buckling [11] or liner wrinkling for
mechanically lined pipe [10]. JIP for Installation of Rigid
Pipelines [11] shows that available material models in FEA
software significantly overestimate the residual ovality. As the
number of load cycles increase, the difference between FE
simulation results and full-scale test measurements increases
[14][26]. Therefore, the one-load material stress-strain relation
A good model that predicts the real-size pipe ovality is one
that should closely predict real test results. Laboratory material
tests for modelling, calibration, and validation have been
conducted. These small-scale tests include several types of
loadings composed of tensile tests and constant amplitude low
cycle fatigue tests (LCF) up to 3% strain level to mimic the
process of reeling. The experimental results and the stress-strain
response of FE predictions have been compared. The material
model verification and validation have shown that the proposed
material model is robust for multi-cyclic reeling analysis. The
accuracy of the prediction was acceptable. To further examine
the accuracy of this material model, full-scale pipe bending tests
were also carried out.
Relevant test data were established in a material property
database written in Python and implemented into Saipem's inhouse pipeline simulation framework Subsea Pipeline
Development (SPIDEV) [6].
2
PARAMETER-BASED MATERIAL MODEL
To deal with the material under cyclic loading, the Abaqus
combined hardening model is described by the theory of flow
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The rigid pipelay reel lay method is an efficient way to
install subsea pipeline used for several decades now with an
extensive track-record. It does however introduce plastic
deformation to the product which must be effectively managed
as shown in earlier reeling studies from installation contractors
[13][19][20] or from manufacturers [12][22]. To date there is still
no extensive reference nor consensus on the material model to
be used for CS seamless pipe as various approaches are recently
reported [14][23][26].
is not suitable for modelling pipeline subject to reeling [17].
Although the research on the constitutive relationship is
advanced [18], the Finite Element Analysis software provides
limited solutions. Abaqus provides a build-in combined
hardening model based on Chaboche plastic constitutive model
describing the constitutive relationship of metal material under
cyclic loading [1]. However, the Abaqus build-in combined
hardening material cannot build of different shapes for the first
load (half-cycle), typically with Lüders plateau for carbon steel,
to a stabilised hysteresis loop. For seamless pipe, Lüders plateau
modify material response and need to be captured [18][21].
Further, material response to cyclic loads is not sufficiently
captured; the stress-strain curve response for the first load and
relaxation is similar to the one for the next cycle. One solution is
to utilise a User Subroutine and utility routines interfaces
provided by Abaqus to implement a more realistic material
property.
FIGURE 2: YIELD SURFACE SIZE VARIATIONS OVER CYCLES
The equivalent plastic strain is defined as
𝑝𝑝𝑝𝑝
𝜀𝜀̅𝑖𝑖 =
As the combined hardening rule plays an important role in
the parameter-based material model, the combined hardening
model in Abaqus Documentation [1] and related User Subroutine
will be presented in this section.
∆𝜀𝜀 𝑝𝑝𝑝𝑝 ≈ ∆𝜀𝜀 −
Isotropic Hardening
In Abaqus combined hardening model, a non-linear
isotropic hardening part defining the evolution of the yield
surface size 𝜎𝜎 0 in function of an equivalent plastic strain 𝜀𝜀̅𝑝𝑝
was proposed as shown below:
𝑝𝑝
𝜎𝜎 0 = 𝜎𝜎|0 + 𝑄𝑄∞ �1 − 𝑒𝑒 −𝑏𝑏𝜀𝜀� �
(1)
Where 𝜎𝜎|0 is the yield stress when the equivalent plastic strain
equals zero; 𝑄𝑄∞ and 𝑏𝑏 are parameters to be determined means
the maximum change in the size of the yield surface and rate at
which the size of the yield surface changes as plastic strain
𝑝𝑝
increases, can be calibrated through the data pair of �𝜎𝜎𝑖𝑖0 , 𝜀𝜀𝑖𝑖 �;
0
𝜎𝜎𝑖𝑖 is the size of the yield surface in i’th cycle which is defined as
the following equation:
𝜎𝜎𝑖𝑖0 = 𝜎𝜎𝑖𝑖𝑡𝑡 − 𝛼𝛼𝑖𝑖
𝛼𝛼𝑖𝑖 =
𝜎𝜎𝑖𝑖𝑡𝑡 + 𝜎𝜎𝑖𝑖𝑐𝑐
2
(2)
(3)
Where, 𝜎𝜎𝑖𝑖𝑡𝑡 and 𝜎𝜎𝑖𝑖𝑐𝑐 are the maximum tensile stress and the
maximum compressive stress respectively.
1
(4𝑖𝑖 − 3) ∆𝜀𝜀 𝑝𝑝𝑝𝑝
2
(4)
2𝜎𝜎1𝑡𝑡
𝐸𝐸
(5)
Where, ∆𝜀𝜀 𝑝𝑝𝑝𝑝 is the plastic strain range.
Nonlinear Kinematic Hardening
Abaqus combined hardening model defines the back-stress
as a function of plastic strain 𝜀𝜀 𝑝𝑝𝑝𝑝 in a stabilised cycle, as is
formulated in:
𝛼𝛼𝑘𝑘 =
𝐶𝐶𝑘𝑘
𝑝𝑝𝑝𝑝
𝑝𝑝𝑝𝑝
�1 − 𝑒𝑒 −𝛾𝛾𝑘𝑘𝜀𝜀 � + 𝛼𝛼𝑘𝑘,1 𝑒𝑒 −𝛾𝛾𝑘𝑘𝜀𝜀
𝛾𝛾𝑘𝑘
(6)
…where 𝐶𝐶𝑘𝑘 and 𝛾𝛾𝑘𝑘 are hardening parameters to be calibrated.
𝐶𝐶𝑘𝑘 is initial kinematic hardening modulus and 𝛾𝛾𝑘𝑘 is the rate at
which the kinematic hardening modulus varies with increasing
plastic deformation. 𝛼𝛼𝑘𝑘 is kth backstress and 𝛼𝛼𝑘𝑘,1 is kth
backstress of the first data point, 𝑘𝑘 = 1, 2, 3, . . . , 𝑁𝑁.
𝑝𝑝𝑝𝑝
Plastic strain 𝜀𝜀𝑖𝑖
𝑝𝑝𝑝𝑝
𝑝𝑝𝑝𝑝
𝑝𝑝𝑝𝑝
in data pairs �𝜎𝜎𝑖𝑖 , 𝜀𝜀𝑖𝑖 � is defined as
𝜀𝜀𝑖𝑖 = 𝜀𝜀𝑖𝑖 −
𝜎𝜎𝑖𝑖
− 𝜀𝜀𝑝𝑝0
𝐸𝐸
(7)
Where, 𝜀𝜀𝑖𝑖 is the plastic strain value when the curve intercepts
𝑝𝑝𝑝𝑝
𝑝𝑝𝑝𝑝
the strain axis and 𝜀𝜀1 equals zero. For each data pair �𝜎𝜎𝑖𝑖 , 𝜀𝜀𝑖𝑖 �,
backstress could be obtained from:
V003T04A024-3
𝛼𝛼𝑖𝑖 = 𝜎𝜎𝑖𝑖 − 𝜎𝜎 𝑠𝑠
(8)
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combining the yield condition, in which the Mises yield rule is
applied, the associated flow rule, and Lemaitre and Chaboche
isotropic / kinematic strain hardening rule [15]. A hardening rule
describes how the yield surface changes with plastic
deformation. Numbers of hardening rules have been proposed
since Prager created the first linear kinematic hardening model
in 1956 [25]. Among these two conceptions are widely adopted:
isotropic hardening and kinematic hardening. Isotropic
hardening signifies the yield surface, keeps the same shape under
cyclic load and expands with increased or decreased stress.
Kinematic hardening describes a hardening where the yield
surface remains the same shape as well as its size but translates
in stress space by a stress 𝛼𝛼, named backstress. Lemaitre and
Chaboche [15] established that the plastic behaviour of materials
can be effectively described by the combined model of isotropic
and kinematic hardening rather than only one of them. They
decomposed the backstress into several components to improve
the description of transient hardening behaviour. It has been
found to be suitable for modelling the behaviour of steel based
on the results of the tests [12][14][16][17][20].
…where, 𝜎𝜎 𝑠𝑠 = (𝜎𝜎1 + 𝜎𝜎𝑛𝑛 )/2.
Abaqus User Subroutine
From the study of the material subjected to reeling, some
features can be highlighted to help drawing a systematic
approach (FIGURE 3).
3
MATERIAL TEST AND ANALYSIS
3.1
Test materials and test types
Data for the material model was collected from a series of
small-scale Tensile and Cyclic tests performed by a UKAS [27]
accredited laboratory. The samples were made from 16’’ OD
SMLS L450Q PSL2 pipe joints (named DNV450 later). Other
pipe joints from the same batch were used for full-scale bending
trials so the data can be used for a material model and bending
trial FEA simulation comparison.
Specimens T1 to T3 were tested under monotonic loading.
Specimens C1 to C10 were tested under different kinds of cyclic
loading to investigate the hysteretic behaviour and constitutive
characteristics. All testing was performed using Zwick and
Instron test machines and explored the following straincontrolled loadings shown in TABLE 1 including a failure (C6).
Specimen
Test type
Straining
Applied Cycle
T1
T2
T3
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
Tensile
Tensile
Tensile
Cyclic
Cyclic
Cyclic
Cyclic
Cyclic
Cyclic
Cyclic
Cyclic
Cyclic
Cyclic
Full curve to break
Full curve to break
Full curve to break
+/- 0.5%
+/- 0.5%
+/- 1.0%
+/- 1.0%
+/- 1.5%
+/- 1.5%
+/- 2.0%
+/- 2.0%
+/- 3.0%
+/- 3.0%
10
10
10
10
10
Failure
10
10
10
10
TABLE 1 SUMMARISED LIST OF SMALL-SCALE TEST PROGRAMME
FIGURE 3: FLOW CHART OF USER SUBROUTINE IN PARAMETERBASED MATERIAL MODEL
Firstly, it’s known that the pipeline is under displacement control
in which the nominal strain can be pre-calculated. Secondly, the
strain values on the pipe extrados and intrados are approximately
symmetrical, while one is in tension another one is in
compression. By these assumptions, a tailored material model
for reeling is created. This method was incorporated into
ABAQUS by coding a User Subroutine. In the subroutine, the
stress-strain curves are assigned by the material field. The initial
material state is defined as the predefined material field. It is then
revised in cycles with the material property derived from preacquired calibrated test data. These stress-strain relations are
activated in the corresponding loading cycle. The relevant
material property is changed from cycle to cycle using field
variables representing the number of loading cycles by
Note that the positive and negative signs mean tension and
compression respectively.
3.2
No-Standardized specimen geometry
To standardise testing as far as possible, conditions
according to BS EN ISO 6892-1 [4] for tensile tests and BS-7270
[5] for low cycle fatigue tests were followed. One significant
change to specimen geometry was applied across all tests
because some tests required full tensile curves following cyclic
straining. Therefore, specimens were cut to the round bar
geometry outlined in [5] for low cycle fatigue. This approach
was verified before the start of the programme by performing 2
tensile tests according to BS EN ISO 6892-1 geometries and 2
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𝜎𝜎 𝑠𝑠 is the stabilised size of the yield surface, i.e., an average
value of the first data 𝜎𝜎1 and last data 𝜎𝜎𝑛𝑛 . Lots of data pairs
𝑝𝑝𝑝𝑝
�𝜎𝜎𝑖𝑖 , 𝜀𝜀𝑖𝑖 � were used to calibrate the parameters 𝐶𝐶𝑘𝑘 and 𝛾𝛾𝑘𝑘 .
USDFLD. Several sets of field variables are used also to fit to
the corresponding material property.
3.3
Specimen loading and test machine control
Whilst the standards provide guidance on strain rates, these
were rationalised to represent material from the extrados and
intrados during full-scale simulated reeling trials. In the case of
cyclic straining short pauses were added before load reversal in
order not to overheat the specimen. The tests were performed at
a laboratory ambient air temperature of approximately 23oC.
In all test cases, strain control for the Zwick and Instron test
machines was provided using the appropriate clip-on extensomer
which was datalogged as well as the crosshead load. For most
tests, a twin camera Digital Imaging Correlation system was also
used to get 3 virtual strain gauges along the left, centre and right
side of the specimen but it was not used for load control.
FIGURE 4: DIC IMAGES, LCF SPECIMEN WITH VIRTUAL GAUGES
(LEFT), UNIFORM STRAINING DURING ELASTIC LOADING (CENTRE) AND
STRAIN CONTOUR DURING PLASTIC LOADING (RIGHT)
Not all cyclic tests were successful, and adaptations were
applied throughout the process based on lessons learned. Each
test typically contained 5 tests of the same load case. Whilst
some tests were rejected due to visible buckling, sufficient data
was obtained to show repeatability and give confidence in the
test results. A small selection of ±3% specimens post-straining is
shown in FIGURE 5.
Whilst tensile testing was straightforward, an additional
complication for the cyclic fatigue tests was the prevention of
buckling in compression past a critical threshold for strain. Some
changes were made to reduce specimen size or to the test set-up.
This was favoured since buckle arrestors on the specimen would
have restricted the access for the analogue extensometer and
reduced the visibility for the DIC cameras.
3.4
On-test measurements
The DIC system allowed to obtain additional strain
information from the axial and circumferential directions by the
application of “virtual” biaxial strain gauges and extensometers.
DIC also allowed better determination of any bending of the
specimens when loaded in compression. Prior to deployment, the
DIC system went through a period of validation comparing the
absolute readings against traditional bonded strain gauges. It
was shown to be more reliable at higher strains with slightly
smaller cumulative drift in readings over multiple cycles.
An additional benefit of the use of DIC (though not a
specific criteria for these tests) is to be able to replay the DIC
video file with the strain map overlaid as shown in FIGURE 4.
This demonstrates well the elasto-plastic transition in the
specimen as one area work hardens, the yielding transfers to the
next weakest point in the crystalline structure.
FIGURE 5: SOME SPECIMENS AFTER ± 3% SYMMETRICAL CYCLIC
LOADS WITH VARIOUS DEGREES OF RESIDUAL DEFORMATION
3.5
Test Results and Analysis
Whilst failed tests due to specimens buckling could be
identified during the testing activities, the quality of individual
stress-strain and loading curves from each of the measurement
data files for each “successful” were evaluated.
Monotonic Behaviour
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tensile tests with geometry according to BS-7270. Comparisons
were made of the Young’s Modulus (elastic region), work
hardening (plastic region) and any adverse effect due to the
reduction of cross-section (necking) between the 4 tests. The two
geometries produced sufficiently comparable results allowing
for natural variations in test materials and acceptable measuring
accuracies between tests.
Hysteretic Behaviour
The responses of the material under cyclic loading from C1
to C10 are shown from FIGURE 7 to FIGURE 11. The hysteretic
behaviour of DNV450 is clearly seen. By constant-amplitude
cyclic loading, the material shows a typical cyclic hardening
shape though the hardening is not significant. For specimens C1
to C4 within a small straining range, the peak stress slightly
increases cycle after cycle. For specimens subjected to higher
straining, the peak stress firstly increases after the first loading
cycle then decreases following hysteretic cycles leading to a
strength decrease. A focus on peak strain for each hysteric cycle
is shown in FIGURE 12. It can be explained by the specimen
slightly buckling. For all the specimens, the tensile nominal yield
stress is nearly the same as the one derived in monotonic loading.
The stress-strain curve response showed combined
hardening behaviour including isotropic hardening and nonlinear
kinetic hardening; the Bauschinger effect of the material is
observed.
FIGURE 7: C1 SAMPLE STRESS-STRAIN CURVES UNDER CYCLIC
LOADING
FIGURE 8: C3 SAMPLE STRESS-STRAIN CURVES UNDER CYCLIC
LOADING
FIGURE 6: MATERIAL STRESS-STRAIN CURVE UNDER MONOTONIC
FIGURE 9: C5 SAMPLE STRESS-STRAIN CURVES UNDER CYCLIC
LOADING
LOADING
Specimen
f0.2/MPa
fu/MPa
εu/%
T1
528
606
9.7
T2
529
611
9.5
T3
527
606
9.5
TABLE 2 TEST RESULTS FOR MONOTONIC LOADING
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Stress-strain curves of monotonic loading are shown in
TABLE 2 . Trimming of result data to get a smooth curve is
applied. As the results were found to be quite similar, only one
result is presented in FIGURE 6. The nominal yield strength is
about 530 MPa, and the ultimate strength is about 610MPa for
these samples.
FIGURE 10: C7 SAMPLE STRESS-STRAIN CURVES UNDER CYCLIC
LOADING
FIGURE 13: KINEMATIC HARDENING MODEL CALIBRATION WITH
THREE BACKSTRESSES
Straining
𝐶𝐶1
+/- 0.5%
7.11E+10
+/- 1.0%
+/- 1.5%
γ1
γ2
𝐶𝐶2
𝐶𝐶3
γ3
435.3
1.6E+11
2429.7
1.54E+11
8943.8
7.55E+10
2690
4.4E+10
688.0
1.57E+10
127.6
2.81E+11
15991
1.3E+10
322.4
7.57E+09
58.0
+/- 2.0%
4.82E+09
55.03
1.1E+11
2175.1
3.47E+10
402.9
+/- 3.0%
1.55E+09
21.06
5.4E+10
1187.4
1.69E+10
216.5
TABLE 3 PARAMETERS IN COMBINED HARDENING MODEL
FIGURE 12: C7 SAMPLE, PEAK STRAIN IN TENSION FOR VARIOUS
CYCLES (DETAIL)
3.6
Parameter Calibration
The stress-strain curves obtained in the cyclic loading tests
were used to calibrate Chaboche kinematic hardening parameters
Ci and γi [15]. The calibration of parameters was carried out for
stabilised cycle following the procedure presented in Abaqus
documentation [1].
A three-backstress model is used. The first one corresponds
to the linear/elastic part of the curve; the second one represents
the transient nonlinearly part of the curve and the last one starts
hardening with a very large modulus and stabilises quickly. The
parameters were found for each straining step and tabulated in
TABLE 3. Good agreements between testing and generated
backstress curves were achieved. FIGURE 13 presents an
example of a 2% straining case.
Numerical simulation of the material tests
The hardening parameters obtained from the small-scale
analysis were used in the subsequent ABAQUS analyses. The
parameter-based material model was first tested with a 3-D solid
single-element FEA model. The comparison between the FE
results and small-scale test results is presented in FIGURE 14 to
FIGURE 18.
The simulated curves are in good accordance with the
experimental curves in accordance with the straining level. The
simulation predicts reasonably well the first load and the cyclic
cycle and fits well for the first load. In some cases, the transient
part of elastic/plastic is stiffer than experimental counterpart.
The FE results overestimate the stress in certain strain regions
due to some unknown imperfection in the test. The prediction
strongly depends on the quality of the data used for calibration.
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FIGURE 11: C9 SAMPLE STRESS-STRAIN CURVES UNDER CYCLIC
LOADING
FIGURE 18: EXPERIMENTAL AND FE CURVES, CYCLIC STRAINING
±3.0%
4
FULL-SCALE SIMULATED REELING TEST AND
ANALYSIS
Data for subsequent full-scale reeling Abaqus model
validation were collected from full-scale reeling simulation trials
performed by an experienced testing contractor.
FIGURE 15: EXPERIMENTAL AND FE CURVES, CYCLIC STRAINING
±1.0%
4.1
Test string configuration
Full-scale reeling simulation test strings were prepared from
16” OD x 21.4mm CS SMLS L450 Q PSL2 of approximately
12.0m length. All material was from the same manufacturing
batches as used for the small-scale testing programme. The test
strings had no weld or any other features in them.
4.2
FIGURE 16: EXPERIMENTAL AND FE CURVES, CYCLIC STRAINING
±1.5%
Full-scale reeling simulations
Reeling simulations were performed using a servo-hydraulic
test machine with a reeling former radius of 8.0m (Saipem
Constellation reel hub radius) and a straightening former radius
of 66.0m. The later was selected to bring final straightness close
to the requirement in DNVGL-ST-F101 [7].
The former indentation method was used in this test. That
means rigid formers (marked in yellow in FIGURE 19) are free
to move in the direction perpendicular to the pipe: the pipe is
bent by moving the appropriate former against the pipe. Two
bending cycles are applied to the test simulating one full reeling
cycle. Each cycle was composed of “Reeling”, “Straightening”
and “Relaxed” steps. Note that a nominal back-tension is applied
to stabilise the test string in the machine clamps.
FIGURE 17: EXPERIMENTAL AND FE CURVES, CYCLIC STRAINING
±2.0%
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FIGURE 14: EXPERIMENTAL AND FE CURVES, CYCLIC STRAINING
±0.5%
Value
Reeling radius
8.0m (7.8m average measured)
Straightening radius
66.0m (64.6m average measured)
Bending cycles
2
Bending steps
6
Back tension
10kN
Bending former length
6.4m
Manual measurements of all test strings were collected for
length, straightness, wall thickness and (external) ovality across
the cardinal points at regular spaced intervals along the reeled
length. With the exception of wall thickness, all measurements
were taken in pre- and post-reeled conditions.
4.4
TABLE 4 SUMMARY OF REELING SIMULATION PARAMETERS
The reeling test rig was operated in an “extended”
configuration with longer former contact lengths and an
additional load was applied to each pipe end creating an end
torque around the outer pivot pins.
FIGURE 19: FULL-SCALE
REELING
SIMULATION
TEST
RIG
ARRANGEMENT
The outer loads applied were below the plastic bending
moment and reduce the contact load applied by the formers in
the middle. The outer torque produced a bending lever length
closer to full-scale operations and a more representative ovality.
All displacements and loads applied to the pipe are continuously
datalogged as well as the ambient air temperature inside the test
hall. The test rig configuration is shown in FIGURE 19 with a test
string in fully reeled load condition shown in FIGURE 20.
On-test measurements
“On-test” data was collected by moving the bending formers
to pre-calculated points, then pausing and additional
measurements taken along the fully reeled length building up the
total number of measurements as shown in TABLE 5. In addition,
bonded strain gauges were positioned at equally spaced positions
along the reeled length to capture set strain at the intrados and
extrados. Additional gauges were placed at the 12 and 6 o’clock
positions to give strain on the neutral axis. The “on-test” ovality
data was collected along the representatively reeled length using
a “Snap-On” laser fitted to an iPEK inspection rover. This system
produced a readout of internal ovality to ASTM which was later
converted to external DNV ovality using the cartesian coordinates and the manual wall thickness measurements taken.
Cycle
step
Straightness
External
ovality
Wall
thickness
Internal
ovality
scan
External
scan
Initial
pre-test
X
X
X
X
X
Reeled-1
X
X
Straighte
ned-1
X
X
Relaxed1
X
X
Reeled-2
X
X
Straighte
ned-2
X
X
X
X
Relaxed2
X
X
TABLE 5 FULL-SCALE REELING SIMULATION TEST MEASUREMENTS
The “on-test” external scans were performed using the same
DIC system as the small-scale laboratory tests but with 2 pairs of
cameras each fitted to computer-controlled linear rails traversing
the length and width of the formers in a pre-programmed arc as
shown in FIGURE 21.
FIGURE 20: FULL-SCALE REELING SIMULATION IN PROGRESS
4.3
Dimension measurements
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Parameter
Ovality
Recall that DNV ovality is defined as in the equation below:
𝑂𝑂 =
FIGURE 21: QUAD CAMERA DIC SYSTEM FITTED TO UNDERSIDE OF
REELING SIMULATION TEST MACHINE
One pair of cameras traverses the side of the pipe at the
intrados with the other pair traversing the extrados side. The
system provides coverage of the bottom half of the pipe skin
along the centre 3.0m of the representatively reeled length. The
DIC system had previously undergone extensive validation using
reeled material fitted with bonded strain gauges. The results
between the two were shown to have sufficient overlap within
measuring accuracies from each of the techniques. However,
since these were the first full-scale simulated reeling trials
performed using DIC for Saipem, strain data was directly
compared between the gauges and DIC readings to build further
confidence for other reeling trial test programmes.
𝑂𝑂𝑂𝑂𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑂𝑂𝑂𝑂𝑚𝑚𝑚𝑚𝑚𝑚
∙ 100%
𝑂𝑂𝑂𝑂𝑛𝑛𝑛𝑛𝑛𝑛
(9)
By internal scanning, the internal pipe coordinates after each
bending step are logged. Using this data, DNV ovality along the
pipe is shown step by step in FIGURE 23 in which the pipe centre
is taken as zero. Approximately 7m pipe length was scanned each
time.
FIGURE 23: DNV OVALITY ALONG PIPE LENGTH (FROM
MEASUREMENTS)
Strain by Heatmap
The DIC provides local strain results in function of a 3Dimensional coordinates. In this study, the local strain is
visualised by Plotly [23] as coloured rectangular tiles in function
of the pipe length (X) and angular position (Y) as shown from
FIGURE 24 to FIGURE 29. Positive strain means strain in tension,
while the negative means compression.
FIGURE 22: PIPE TEST STRING AFTER TESTING
4.5
Post-test Data Processing
The ovality and DIC scans produce significant quantities of
raw data which requires post-processing before comparison with
the FEA reeling model. The choice of ovality scanning tooling
also means that geometrical corrections are applied to the ovality
obtained to allow for the adverse effect of the change in geometry
inside the pipe because of curvature. The generated test data is
compared to the Abaqus simulation results.
4.6
According to the position of the DIC cameras, the angular
coverage is around 150 degrees of the pipe circumference, going
from a value around 3 o’clock up to approximately 9 o’clock.
Only parts of the pipe section can be scanned during the bending
trial due to the presence of obstacles (such as bending formers).
As mentioned previously, bonded strain gauges were applied
also to build confidence in the DIC system. Wiring of these
gauges inevitably left “shadows” on the pipe shown as white
areas on the DIC heat maps.
Results and Analysis
As the bending former length is smaller than the pipe length,
during the bending-on steps the end of the former creates high
deformation of the pipe which should be ignored in the study.
V003T04A024-10
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It is also well known that the centre of the bending rig produces
higher contact stresses and ovality. To this end only the crosssections at +/-1.25m from the centre are considered for
comparison of ovalities.
FIGURE 25: HEAT MAP OF LONGITUDINAL STRAIN; 2ND STEP,
FULLY BENT ON STRAIGHTENER FORMER
FIGURE 28: HEAT MAP OF LONGITUDINAL STRAIN; 5TH STEP,
FULLY BEND ON STRAIGHTENER FORMER
FIGURE 29: HEAT MAP OF LONGITUDINAL STRAIN; 6TH STEP,
RELAXATION
3D Scatter Strain
Similar to the heat maps from the Cartesian coordinates
obtained, a 3-D Scatter pipe representing the coloured scale
strain value was plotted to show the interactive results and help
the user to easily check the data points.
FIGURE 26: HEAT MAP OF LONGITUDINAL STRAIN; 3RD STEP,
RELAXATION
FIGURE 30: LONGITUDINAL STRAIN ON 3-D SCATTER, 4TH STEP:
FULL BENDING ON REEL FORMER FOR THE 2ND TIME
FIGURE 27: HEAT MAP OF LONGITUDINAL STRAIN; 4TH STEP,
FULLY BENT ON REEL FORMER
From the full-scale bending tests, the pipe ovality and
longitudinal strain are obtained as shown in FIGURE 23.
Curvature imposed by the bending former is slightly larger at the
ends. Therefore, ovality at the former ends will be disregarded.
The peak ovality at the centre of the pipe is considered. The
curves show an increasing trend by comparing the first cycle to
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FIGURE 24: HEAT MAP OF LONGITUDINAL STRAIN; 1ST STEP,
FULLY BENT ON REEL FORMER
the second one. Similar to the ovality, FIGURE 24 to FIGURE 29
confirm there is consistent axial strain along the intrados and
extrados.
Test
step
Ovality by
int. scan
Ovality by ext.
measurement
Axial. strain
at 9 o’clock
Axial. strain
at 3 o’clock
[%]
[%]
[%]
[%]
1
3.52
-
-1.94
2.42
2
1.35
-
0.53
-0.11
3
1.29
-
-
-
4
3.68
-
-1.89
2.49
5
2.20
-
0.59
-0.03
6
1.95
1.77
-
-
FEM prediction by Parameter-based Material Model
The parameter-based material model is assigned to the
material (cf. TABLE 3). FIGURE 32 presents the FEM steps, from
top to bottom, before bending, bending by the reeling former,
bending by the straightening former and relaxed.
TABLE 6 EXPERIMENTAL MEASUREMENTS AFTER BENDING STEPS
FIGURE 32: FEA MODEL OF THE FORMER INDENTATION BENDING
RIG
FIGURE 31: PIPE POSITION RELATED TO THE BENDING RIG
FEM prediction by Ramberg-Osgood curve
4.7
Prediction of the full-scale bending tests
FE model
The full-scale bending test is simulated by a halfsymmetrical 3-D model. The pipe is composed of three parts
along the pipe longitudinal: at the pipe middle, which has contact
with the formers the first-order linear solid finite element is used,
and refined mesh is applied for the region of interest; at the pipe
DNV JIP [11] suggests a Ramberg-Osgood curve describing
the nominal stress and strain (𝜎𝜎𝑛𝑛 and 𝜀𝜀𝑛𝑛 ) as following:
V003T04A024-12
𝜀𝜀𝑛𝑛 =
𝜎𝜎𝑛𝑛
𝜎𝜎𝑛𝑛
�1 + 𝐴𝐴𝑦𝑦 ∙ � �
𝐸𝐸
𝜎𝜎𝑦𝑦
𝑛𝑛−1
�
(10)
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TABLE 6 summarises the peak ovality obtained by the
internal scan and, at the end of the bending trial, by external OD
measurement. The pipe position related to the bending rig is
illustrated in FIGURE 31. These measurements will be compared
against the FE simulation results in the next section.
“head” and pipe “end”, beam element is used to simplify the
model. The main dimensions of the pipe and the formers are set
as per the test string. At both extremities of the pipe, two nodes
are restrained by Uy, Uz, URx, and URy DOFs and enable them
to move following the pipe axial direction during the bending.
(11)
𝜀𝜀𝑦𝑦 ∙ 𝐸𝐸
𝐴𝐴𝑦𝑦 =
−1
𝜎𝜎𝑦𝑦
(12)
…where 𝜎𝜎𝑦𝑦 and 𝜎𝜎𝑢𝑢 are yield stress and ultimate stress
respectively.
Using this relation, a sensitivity case was performed by a
Ramberg-Osgood curve obtained by the first load of 3%
straining experimental results. The result is presented in the next
subsection.
former of 8.0 m radius and associated straightener radius), it is
anticipated that the JIP formulation shows good agreement with
experimental result presented here.
The manufacturing ovality in the FE simulation is taken as
zero, which is essentially in-line with the test string pre-reeling
measurement. The results are shown in the next subsection.
Comparison and Discussion
FIGURE 33 and TABLE 7 present a comparison between the
ovality in each load step obtained by the test measurements,
DNV JIP criterion, FEM prediction by Ramberg-Osgood curve,
and the FEM prediction by User Subroutine. Both RambergOsgood and build-in combined hardening FE model have been
calibrated against small scale test.
DNV JIP Residual Ovality
Based on the ovality predicted in DNVGL-ST-F101 [7][8],
the DNV JIP [11] proposed a formula to assess the residual
ovality for the pipe size between 12’’ and 16’’ OD and subjected
to large plastic strains under cyclic loading. This will be used to
compare the full-scale test measurements with the FE simulation
results.
The residual ovality due to bend cycle i is defined as:
𝑜𝑜𝑚𝑚𝑚𝑚𝑚𝑚,𝑖𝑖 = �1 + 𝑘𝑘𝑜𝑜,𝑖𝑖 � ∙ �𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖−1 + 𝑜𝑜𝐷𝐷𝐷𝐷𝐷𝐷,𝑖𝑖 �
(13)
𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖 = 𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖−1 + 𝑘𝑘𝑜𝑜,𝑖𝑖 ∙ �𝑜𝑜𝑚𝑚𝑚𝑚𝑚𝑚,𝑖𝑖 − 𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖−1 �
(14)
The subscripts max and res means maximum ovality and
residual ovality; i and 𝑖𝑖 − 1 are actual bend step and the
previous bend step; 𝑘𝑘𝑜𝑜,𝑖𝑖 is the residual ovality factor at the
actual bend cycle, a value in the range of 0.25 to 0.35 for the first
cycle and 0.05 to 0.15 for the subsequent cycles is suggested.
𝑜𝑜𝐷𝐷𝐷𝐷𝐷𝐷,𝑖𝑖 is ovality predicted by the following expression:
𝑜𝑜𝐷𝐷𝐷𝐷𝐷𝐷,𝑖𝑖 = 0.03 ∙ (1 + 𝐷𝐷/120𝑡𝑡) ∙ �2𝜀𝜀𝑏𝑏,𝑖𝑖 ∙ 𝐷𝐷/𝑡𝑡�
2
(15)
Different results can be computed according to the residual
ovality factors applied. In this paper two sets of factors
presenting lower bound (0.25 and 0.05 for the first cycle and the
second cycle respectively) and upper bound (0.35 and 0.15 for
the first cycle and the second cycle respectively) are used in the
ovality calculation.
FIGURE 33: OVALITY RESULTS FROM TESTING AND PREDICTION
It shows that a parameter-based material model predicts a
similar trend to testing; it obtains a good result at the first reeled
step.
In the subsequent step, the computed ovality is higher,
especially in the second fully reeled step. It shall be noted that in
the meantime, the FE model calibration is not finalized yet. The
configuration of the former indentation testing facility is
complex between the fully reeled step to the fully straightened
step: it is composed of several small steps to change the loads
including the pipe end tension and the end torque, as well as the
carriage displacement. The FE model should reflect these
changes as the combination of them can impact the pipe ovality.
At the time of writing, further calibration of the FE model is still
ongoing.
It is to be noted that the DNV JIP [11] refers to the residual
ovality study reported in [13] where a 16’’ OD x 21.4 mm X65
pipe was tested on a bending rig using a 8.0 m reel former. In this
paper, the calibration of the above equation uses the upper bound
values for this pipe and this test. As a similar pipe (same grade,
OD and thickness) has been tested in close conditions (reel
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𝑛𝑛 =
𝜎𝜎𝑦𝑦
𝜎𝜎𝑢𝑢
/
−
𝐸𝐸 � �𝜀𝜀𝑦𝑦 𝐸𝐸 ��
𝑙𝑙𝑙𝑙𝑙𝑙�𝜎𝜎𝑢𝑢 /𝜎𝜎𝑦𝑦 �
𝑙𝑙𝑙𝑙𝑙𝑙 ��𝜀𝜀𝑢𝑢 −
Step
Exp.
JIP Upper
FEM R-O curve
FEM UserSubroutine
[%]
Δ
[%]
Δ
[%]
Δ
1
3.52
4.2
19.3%
3.21
-8.8%
3.39
-3.7%
2
1.35
NA
NA
1.74
28.9%
1.74
28.9%
3
1.29
1.5
16.3%
1.64
27.1%
1.61
24.8%
4
3.68
5.2
41.3%
4.36
18.5%
4.47
21.5%
5
2.20
NA
NA
2.90
31.8%
2.81
27.7%
6
1.95
2.0
2.6%
2.80
43.6%
2.69
37.9%
TABLE 7 COMPARISON OF PRELIMINARY OVALITY RESULTS
Depending on the residual ovality factors applied, the DNV
JIP formulation can get closer results to the test measurement
considering the upper bound parameters for the relaxed step;
especially when using the parameters used for calibration for 16’’
pipe [11][13]. However, it overestimates fully reeled step.
5
CONCLUSION
In this paper, experimental and numerical studies have been
carried out to develop a procedure to simulate the material
behaviour of a pipeline under reeling. As a key feature in this
procedure, a parameter-based model was set-up using Abaqus
build-in combined isotropic/non-linear kinematic hardening
model related to the field variable defined in Abaqus User
Subroutine USDFLD and UHARD.
Experimental investigation of DNV450 under monotonic
loading and cyclic loading was performed. Combined hardening
parameters were obtained by these tests and the stress-strain
relations were simulated using parameter-based material model,
which fit well with the experimental curves. Full-scale bending
tests of 16” DNV450 SMLS pipe were also conducted to verify
the performance of the material model. Internal scanning and
DIC cameras were set-up to capture the variation of the
diameters and strains during the tests. FE simulation using
parameter-based material model have been performed. The
results have been compared to the results obtained by DNV JIP
residual ovality criterion and FEM prediction by RambergOsgood curve. The material model developed predicts generally
better results than the Ramberg-Osgood model and gets close
results when comparing the first bending step and conservative
results in the subsequent cycles. In the meantime though,
The material model allows calibration based on the
parameters obtained by small-scale tests under various straining
levels. It can rebuild the shape of the stress-strain relation of
loading cycles and tell the difference between the first load curve
and stabilised hysteresis loop. It also includes discontinuity
such as Lüders plateau to better fit the real case. It is a
straightforward and efficient material model with simple
calibration and avoids complicated UMAT to rebuild constitutive
relations.
Saipem has started the testing program in 2020; the work
presented in this paper is part of it. More full-scale tests with
more loading cycles are being undertaken in order to verify the
cyclic effect of the material model. It shall also be noted that the
current material model does not account for any effect from
temperature. Further works are planned to cover temperature
dependence on material response so that the material model can
cover a wider range of applications.
ACKNOWLEDGEMENTS
Test campaigns have been performed thanks to the support
of Saipem group. The authors would like to express their thanks
to Doosan Babcock for performing the mechanical testing.
Sincere thanks also to Mr. Vincent Cocault-Duverger and Dr.
Shulong Liu, who are greatly thanked for their collaborations on
the material modelling presented here. Their dedicated and
inspiring suggestions are very appreciated. The authors also
thank Mamadou Ahmed-Kogri for processing of the DIC data.
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