Effect of Limit State Design on the Damage Tolerance of ...€¦ · The riser fatigue demand is...
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Transcript of Effect of Limit State Design on the Damage Tolerance of ...€¦ · The riser fatigue demand is...
Effect of Limit State Design on the Damage Tolerance of Subsea Systems
Lee Tran, Mark Cerkovnik 2H Offshore Inc.
Houston, TX, USA
ABSTRACT
Risers, flowlines and other subsea components may be designed using
limit state concepts, where displacement controlled loads are allowed to
push stresses beyond yield. However, there can be consequences if the
lines are damaged or degraded in service. This paper presents a case
study comparing the damage tolerance capacity of a deepwater steel
catenary riser (SCR) designed with allowable (working) stress criteria
and another designed with limit load criteria. The exercise is also
conducted for a production flowline. The damage scenario examines
the effects of various levels of pitting corrosion and accounts for the
potential of accelerated crack growth due to corrosive effects.
KEY WORDS: Fatigue; Limit State Design; Damage Tolerance;
Risers; Flowlines; Finite Element Analysis (FEA); Internal Flaws;
Crack Face Pressure; Fitness for Service.
INTRODUCTION
In recent years, structural design has been moving from allowable
stress design to limit state design concepts. In general, the two methods
of design arrive at the same design solution. However, where loads are
displacement controlled, the limit state approach permits stresses to go
beyond those allowed by the allowable (working) stress method. This is
occasionally observed in risers and flowlines when displacement
controlled loads from vessel motions or thermal expansion are allowed
to push stresses beyond yield. These designs use ductile materials in
their construction and the structure can tolerate such loading when they
are new. This approach is sound and usually allows a thinner and more
economic design as long as the pipe stays relatively unflawed.
However, throughout the life of these components damage or
degradation can occur through service or accident. For example,
damage may come from corrosion pitting, dropped objects, or erosion.
In both steel catenary risers (SCRs) and flowlines, it is common for the
highest loading to occur due to a controlled displacement. As such, the
pipe stresses may safely exceed yield stress due to the ductility of the
steel. In the case of both risers and flowlines, the loading may occur
either early or late in life. Subsea production flowlines are often
designed to buckle in a controlled manner to accommodate thermal
expansion. The curvature from the displacement combined with
misalignment and pressure effects can take the stress in the wall above
yield. It is not uncommon for such lines to cycle from the extremes of
production to shut-down several times a month. Steel catenary risers
may see stress above yield during extreme storms. Since the catenary
shape enforces stability and the strains are the result of the
displacements of the supporting vessel, the strains are controlled.
Risers are fundamentally dynamic structures and as such are subject to
fatigue loadings. Most fatigue analysis assumes the risers are in their
as-designed condition. If corrosion is taken into account in design, it is
by way of assuming a thinner wall. Typically, the reduction is assumed
to be half the corrosion allowance. However, most instances of real
world corrosion occur as pitting or localized wall loss and contribute
stress concentrations that have much more impact on fatigue life than
the loss of a few millimeters of wall thickness. This is also true for
other physical damage, such as a gouge or a dent.
In these cases, the most critical threat to the structure is not pressure
and burst, but rather cyclic loading and fatigue. Consequently, the
fitness for service of the riser or flowline is a fatigue crack growth
assessment with end-of-life coming via fracture or plastic collapse from
the imposition of the extreme load on the section that has grown a
fatigue crack.
In this paper, the difference in damage tolerance of a riser and a
flowline designed with limit state criteria is compared to that of a line
designed to allowable stress criteria. The case studies are taken from
realistic designs of risers and flowlines in the Gulf of Mexico. The
objective of this study is to illustrate the degree to which the extreme
loading condition affects the damage tolerance on risers and flowlines.
In order to assess damage tolerance, the methodologies of API 579-
1/ASME FFS-1 Fitness for Service and BS7910 are employed.
A fitness for service assessment is conducted for two SCRs hung-off a
semi-submersible. One riser is designed to meet an allowable stress
design criteria, and the second is allowed to exceed yield in a
displacement controlled loading. The risers are assumed to have been
subjected to pitting corrosion early in life.
A parallel study is conducted for a pair of subsea flowlines. The first is
designed first to stay below yield. The second is allowed to exceed
yield. Again, the flowlines are subject to various levels of pitting
corrosion
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The two structures provide contrast in terms of their fatigue histograms.
The riser fatigue demand is dominated by many small stress cycles
while the flowline observes relatively few cycles, but the stress range
per cycle is high. The methodology uses finite element analysis (FEA)
tools as well as classical fracture analysis to predict the rates of crack
growth and arrive at predictions of remaining life. Once corrosion
begins and pits form, the structure is challenged by an increase in crack
growth rate caused by the influence of the chemistry on the steel and by
the stress effect of the pit geometry. In high pressure lines, the
influence of crack face pressure must be accounted for. Further
complications arise if extreme storms cause riser stresses to exceed
yield, which then requires the use of strain based methodology.
RISER DESIGN PARAMETERS
The example riser is situated in 1844m water depth in the Gulf of
Mexico (GoM). It is supported by a semi-submersible and hung off
with a flexjoint. The vessel general layout is shown in Figure 1.
Figure 1. General vessel direction specifying both vessel orientation
and positive vessel axis definitions for FEA
The subject riser is a 10in production riser with a wall thickness of 34
mm. The physical parameters of the riser are provided in Table 1. The
hydrodynamic parameters used in the analysis are:
• Unstraked region: Cd=0.84 to 1.2, Ca=1.0
• Straked region: Cd=1.6 to 1.84, Ca=2.0
Marine growth is accounted for in the top 140 m of water depth. The
density of the marine growth is 1045 kg/m3 with a thickness varying
from 2 mm to 25 mm.
Table 1. Steel catenary riser physical parameters, stress concentration
factor (SCF) and crack tip opening displacement (CTOD)
Parameter Value
Outer Diameter 10.75 in (27.31 cm)
Inner Diameter 8.10 in (20.57 cm)
Wall Thickness 1.33 in (3.37 cm)
Riser Azimuth (with respect to
vessel +surge and measured
counterclockwise)
10 deg
Hang off Angle 12 deg
Material 70X
Material Yield Stress 70 ksi (482.6 MPa)
Material Tensile Stress 82 ksi (565.4 MPa)
Internal Corrosion Allowance 5 mm
Wall Thickness Tolerance +/-10 %
Shut-in Pressure at MWL 0 psi (0.0 MPa)
Internal Fluid 43.7 pcf (700 kg/m3)
Pipe Density 490 pcf (7850 kg/m3)
Insulation Thickness 2.36 in (6.0 cm)
Insulation Density 48.8 pcf (782 kg/m3)
Strake Thickness 0.79 in (2.0 cm)
Strake Density 71.7 pcf (1148 kg/m3)
Straked Length at Top 3000 ft (914 m)
Poisson’s ratio 0.3
Flexjoint Weight in Air 32.8 kips (14.9 tonne)
Flexjoint Weight in Water 28.8 kips (13.0 tonne)
Flexjoint Taper Length 19.5 ft (5.94 m)
Flexjoint Start OD 12.0 in (0.305 m)
Flexjoint Stiffness 50.8 kip-ft/deg (68.8 kNm/deg)
SCF at Parent Metal 1.0
SCF at Weld 1.2
CTOD at Parent Metal As specified in Methodology
CTOD at Weld As specified in Methodology
The wave loading is based on general GoM metocean data for the 100-
yr hurricane event. The extreme wave in this study is applied in the
near direction (190 degrees clockwise with vessel surge) in-plane with
the SCR and provided below:
Limit state criteria (100-yr Hurricane)
HS= 16.0 m
TP= 16.6 sec
Hmax=28.0 m
THmax= 15.8 sec
Associated Current
Surface : 2.10 m/s
Depth of zero current 80m
The allowable stress method of design is based on the elastic theory in
which steel are assumed to be stressed well below its elastic limit under
the design loads. Allowable stress is usually a factor of yield stress. In
limit state design the capacity of the section is evaluated with respect to
ultimate failure and yield stress is not necessarily a boundary. Two
scenarios are explored during this study as described below:
1. (Allowable stress limited design) Extreme stresses are
controlled to 80% of yield by adding a weight optimized
coating to the riser. The design criterion is 80% of yield in a
100-yr return period event per API 2RD requirements.
2. (Limit state design) Recognizing that the peak hurricane
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stresses are displacement controlled, extra weight is not
added beyond that needed for operational loads. However, the
riser goes into compression and controlled buckling occurs,
during which the riser is stressed to 126% of yield in linear
analysis in the hurricane. Note that in this scenario, the
analysis is also conducted with non-linear material properties
to confirm displacement control and establish the level of
strain in the cross section.
FLOWLINE DESIGN PARAMETERS
The subject flowline in this paper is a 10 inch production flowline with
a wall thickness of 34mm. The detailed design parameters of the
flowline are provided in Table 2.
Table 2. Flowline physical parameters, stress concentration factor
(SCF) and crack tip opening displacement (CTOD)
Parameter Value
Outer Diameter 10.75 in (27.31 cm)
Inner Diameter 8.10 in (20.57 cm)
Wall Thickness 1.33 in (3.37 cm)
Material 65X
Material Yield Stress 65 ksi (448 MPa)
Material Tensile Stress 77 ksi (531 MPa)
Internal Corrosion Allowance 3 mm
Wall Thickness Tolerance +/-10 %
Pressure Range 2100 - 11171 psi
(14.5 - 77 MPa)
Temperature Range 38 – 250 F
(3.3 - 121 C) Internal Fluid 43.7 pcf (700 kg/m3)
Pipe Density 490 pcf (7850 kg/m3)
Poisson’s ratio 0.3
SCF at Parent Metal 1.0
SCF at Weld 1.2
CTOD at Parent Metal As specified in Methodology
CTOD at Weld As specified in Methodology
The loading in the flowline is driven by pressure and temperature
variations. The operational temperature and pressure cause flowline
expansion which is accommodated by controlled lateral buckling.
There are two loadings that are compared in this study and described
below:
Partial start-up/shut down (Allowable Stress)
Temperature range = 106 F (41 C)
Pressure range = 4535 psi (31.3 MPa)
Full start-up/shut down (Limit Load Design)
Temperature range = 212 F (100 C)
Pressure range = 9071 psi (62.5 MPa)
The partial start-up/shut down strain range as 0.2% and the full start-
up/shut down strain is taken as 0.5%.
ANALYSIS METHODOLOGY
Global Loads
Riser dynamic strength analysis is conducted using non-linear time
domain analysis program FLEXCOM-3D from Marine Computation
Services (MCS). The riser is modeled using pipe elements based on
nominal wall properties provided in Table 1.
Refined element meshing at the critical regions of the riser is included.
To meet the allowable stress criteria of 80% of yield for the 100 year
hurricane a weight coating is added in the touch down zone (TDZ) to
control the response. Irregular wave dynamic analysis is used to
confirm the stress levels. For the contrasting case where the weight
coating is not applied the dynamic analysis shows excursion of stress
beyond yield. Hence, nonlinear material properties are used in the SCR
model. The non-linear section properties of the riser are derived from
the material stress strain curve. The analysis shows strain levels below
1%.
Element forces are extracted along the length of the riser and the
location of the maximum moment provides the extreme load for the
damage tolerance analysis. The location of assessment is the critical
section of both the flowline and riser. This correlates to the buckle
crown region of the flowline and the TDZ of the riser.
Damage Tolerance Analysis
While the design codes allow the riser and flowline to push to yield
stress and beyond because of the displacement controlled nature of the
loading, the question remains how the structure can resist damage
because of this additional loading. In conducting the damage tolerance
assessment, the scenario explored is that of corrosion pitting.
In the current methodology, corrosion pits are assessed as planar flaws.
The approach is taken because it is conservative and because fatigue
cracks can nucleate quickly from the bottom of corrosion pits. Also, for
subsea risers and flowlines, it is currently not feasible to verify that
such fatigue cracks are not present using in-line inspection (ILI). It is
also noted that the alternate approach for fatigue assessment; i.e. the SN
approach, requires application of an appropriate SCF which requires
knowledge of the radius at the base of the pit. This information is
generally not available. Furthermore, SN data in corrosive
environments is more difficult to obtain than fatigue crack growth
(FCG) rate data. The degree of conservatism inherent in this approach
is quantified in Urthaler et. al.
It will be seen that in accounting for this threat, fatigue crack growth,
plastic collapse, and fracture must all be addressed. Since the objective
of this work is to illustrate the degree to which moving beyond
allowable stress limits on bending stress affects damage tolerance, only
circumferential flaws are considered.
In the damage tolerance assessment, a flaw is grown by application of
the fatigue load cycles using the appropriate FCG curve. As the flaw
grows, it is checked against the end-of-life load to verify that the
section will not fail. The process is iterated to develop the locus of flaw
sizes that represent a set of allowable initial (AI) flaw sizes. These
results are plotted for the allowable stress design and the limit load
design to compare the effects of the maximum load on the allowable
defect. The method for crack growth determination of end-of-life is
based on API 579-1/ASME FFS-1 criterion. Additionally, the life of the
component is determined for a set of specific assumed initial flaws to
allow a direct comparison of the allowable stress vs. limit load designs
on the basis of life.
During the lifetime of a flowline or riser, both CO2 and H2S can
accelerate fatigue crack growth and should be accounted for during the
analysis. The sweet service FCG curve used is based on the API 579-
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1/ASME FFS-1 criterion for operating in freely corroding marine
environment using mean data + 2 standard deviations and the sour FCG
curve is taken as 6 times the sweet criteria. The two curves are shown
in Figure 2 below.
Figure 2. API 579 FCG Curves in Sweet and Sour Environment
A Level 2B fatigue assessment diagram (FAD) is used based on the
material strength specific stress strain curve. The FAD represents the
fracture limit as a function of load ratio (LR). An example of the FADs
used for the flowline is shown in Figure 3 below. Level 2A is a general
FAD curve that does not use material properties and is provided for
comparison purposes. The material stress-strain relationship is defined
in CSA Z662 and provided below.
( -
) (
)n
(1)
Where,
engineering stress
engineer strain
y = yield stress
A unique n is calculated for the base pipe material as follows:
n
-
(2)
Where,
T = tensile strength
For the weld metal, a Lüder’s plateau is accounted for, and a three part
stress-strain diagram is used:
(3)
( -
) (
)n
Where
n
( -
) (4)
This CSA Z662 stress-strain relationship is further discussed in PRCI
2011.
Figure 3. Fatigue Assessment Diagram for Flowline (65ksi Material)
The cyclic loading for flowlines and risers are derived from different
sources. SCRs are dynamically loaded by vessel 1st and 2nd order
motions, vortex induced vibration (VIV), vortex induced motions
(VIM), slugging, and pressure. On the other hand, flowlines are
dynamically loaded from laterally buckling induced by temperature and
pressure changes from start-up/shut down operations. In this study,
typical design histograms from actual risers and flowlines are used for
crack growth assessment. The fatigue histograms of the riser and
flowline have a distinctly different flavor. The riser fatigue histogram is
made up of millions of small cycles; approximately 6 million cycles per
year from first order vessel motions alone and the flowline is
dominated by ~80 large annual cycles from operational loads.
The load case matrices are is provided for the SCR and the flowline in
Table 3 and Table 4, respectively. The histograms are applied for a
design life of 25 years with a factor of safety of 5 that corresponds to a
sweet service of 17yrs and 8 years of sour. The analysis is conducted
for two levels of assumed toughness. Toughness is measured in terms
of CTOD.
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Table 3. Riser Load Case Matrix
Flaw Depth
(mm)
Flaw Width
(mm) Loading
CTOD
(mm)
3 24
100-yr Hurricane
Additional weight at
TDZ (80% Yield)
0.5
4 32
5 40
6 48
7 56
8 64
3 24
100-yr Hurricane
(0.8% Strain) 0.5
4 32
5 40
6 48
7 56
8 64
3 24
100-yr Hurricane
Additional weight at
TDZ (80% Yield)
0.25
4 32
5 40
6 48
7 56
8 64
3 24
100-yr Hurricane
(0.8% Strain) 0.25
4 32
5 40
6 48
7 56
8 64
Table 4. Flowline Load Case Matrix
Flaw Depth
(mm)
Flaw Width
(mm) Loading
CTOD
(mm)
3 24
0.2% Strain 0.5
4 32
5 40
6 48
7 56
8 64
3 24
0.5% Strain 0.5
4 32
5 40
6 48
7 56
8 64
3 24
0.2% Strain 0.25
4 32
5 40
6 48
7 56
8 64
3 24
0.5% Strain 0.25
4 32
5 40
6 48
7 56
8 64
The computer program 2HFLAW, which is based on API 579-1/ASME
FFS-1, is adopted in the determination of the fatigue crack growth and
unstable fracture behavior of the pits.
FITNESS FOR SERVICE RESULTS FOR THE SCR
The limiting flaw sizes corresponding to the unstable fracture limit for
the parent metal in the riser are shown in Figure 4 where CTOD is
0.5mm. The plot shows a very large difference between the highly
loaded limit state design and the more modestly loaded allowable stress
design. In addition, the plot also shows the allowable initial flaw sizes
that achieve the design life. A flaw defined by a point on this line will
grow to failure in the design life. The allowable initial flaw is a
measure of the damage tolerance of the component. As seen from the
figure, there is only minimal difference between the allowable initial
flaw sizes for the two designs. Similar results are observed in Figure 5
when the CTOD drops to 0.25mm. The allowable initial flaws are only
minimally changed by the higher extreme loading in the limit state
design. For example, for the 50mm wide flaw in parent metal, the
allowable depth is 8.9mm for the allowable stress design, but reduces to
7.5mm for the limit load design.
The weld metal in the riser is assessed in Figure 6 and Figure 7. The
limiting flaw sizes corresponding to the unstable fracture limit for the
riser are shown in Figure 6 where the CTOD is 0.5mm. As expected,
accounting for the SCF and residual stress at the weld causes the
limiting flaws to get smaller. As with the parent metal, the limiting
flaws differ substantially between the allowable stress design and the
limit load design. However, the allowable initial flaw is only slightly
changed by the difference between the allowable stress case and the
limit load case for a CTOD of 0.5mm. In Figure 7, where the CTOD
has dropped to 0.25mm, the influence of the different loading begins to
affect the allowable initial flaw size. For example, for the 50mm wide
flaw in weld, the allowable depth is 7.5mm for the allowable stress
design, but reduces to 4.3mm for the limit load. A summary of
remaining life for the defined flaws of each riser loading case is
provided in Table 5 below. Like the allowable initial flaw, the
remaining life is a measure of the damage tolerance of the component.
The trends seen in Table 5, mirror those seen in the allowable initial
flaw plots.
Flaw growth per year is a function of the histogram observed by the
riser and the fatigue crack growth curve. Hence, crack growth of flaws
for a particular pit under different extreme loadings or CTODs is
identical except for the end-of-life point as shown in Figure 8.
Figure 4. Parent Metal AI Flaw Size Plot – SCR CTOD = 0.5mm
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Figure 5. Parent Metal AI Flaw Size Plot – SCR CTOD = 0.25mm
Figure 6. Weld AI Flaw Size Plot – SCR CTOD = 0.5mm
Figure 7. Weld AI Flaw Size Plot – SCR CTOD = 0.25mm
Figure 8. SCR Flaw Growth of 6x48mm Depth vs. Time Comparison
Table 5. Riser Life Summary
Flaw
Depth
(mm)
Flaw
Width
(mm)
Loading CTOD
(mm)
Parent
Metal
Life
(yrs)
Weld
Life
(yrs)
3 24 100-yr
Hurricane
Additional
weight at
TDZ (80%
Yield)
0.5
2655 1539
4 32 1178 611
5 40 512 277
6 48 249 164
7 56 154 120
8 64 115 98
3 24
100-yr
Hurricane
(Strain
Controlled)
0.5
2644 1499
4 32 1166 572
5 40 499 236
6 48 235 122
7 56 139 74
8 64 99 38
3 24 100-yr
Hurricane
Additional
weight at
TDZ (80%
Yield)
0.25
2655 1539
4 32 1178 611
5 40 512 277
6 48 249 164
7 56 154 120
8 64 115 98
3 24
100-yr
Hurricane
(Strain
Controlled)
0.25
2622 1317
4 32 1147 381
5 40 481 76
6 48 215 10
7 56 119 0
8 64 75 0
FITNESS FOR SERVICE RESULTS FOR THE FLOWLINE
The limiting flaw sizes corresponding to the unstable fracture limit for
the parent metal in the flowline are shown in
Figure 9 where CTOD is 0.5mm. The plot shows a very large
difference between the highly loaded limit state design and the more
modestly loaded allowable stress design. In addition, the plot also
shows the allowable initial flaw sizes that achieve the design life. The
allowable initial flaw is a measure of the damage tolerance of the
component. Unlike the riser, the flowline shows the influence of the
higher loading of the limit state design on the allowable initial flaws. In
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fact the difference is quite sizable. For example, for the 50mm wide
flaw with a CTOD of 0.5mm, the allowable depth is 12.4mm for the
allowable stress design, but reduces to 7.5mm for the limit load design.
Similar results are seen in Figure 10 when the CTOD drops to 0.25mm.
The weld metal in the flowline is assessed in Figure 11 and Figure 12
for CTOD of 0.5mm and 0.25mm, respectively. As expected,
accounting for the SCF and residual stress at the weld causes the
limiting flaws to get smaller. Unlike with the parent metal, the limiting
flaws do not differ substantially between the allowable stress design
and the limit load design. This is because the SCF and residual stress
raise the effective stress in the allowable stress design up to values
similar to that seen in the plastically designed flowline. The allowable
initial flaw is slightly changed by the difference between the allowable
stress case and the limit load case. In Figure 12, where the CTOD has
dropped to 0.25mm, the influence of the different loading is reduced
both in the limiting flaw and in the allowable initial flaw. A summary
of remaining life for the defined flaws of each riser loading case is
provided in Table 6 below. Like the allowable initial flaw, the
remaining life is a measure of the damage tolerance of the component.
The trends seen in Table 6, mirror those seen in the allowable initial
flaw plots.
Similar to the riser, flowline flaw growth per year is a function of the
histogram observed by the flowline and the fatigue crack growth curve.
Hence, crack growth of flaws for a particular pit under different
extreme loadings or CTODs is identical except for the end-of-life point
as shown in Figure 13.
Figure 9. Parent Metal AI Flaw Size Plot – Flowline CTOD = 0.5mm
Figure 10. Parent Metal AI Flaw Size Plot – Flowline CTOD = 0.25mm
Figure 11. Weld AI Flaw Size Plot – Flowline CTOD = 0.5mm
Figure 12. Weld AI Flaw Size Plot – Flowline CTOD = 0.25mm
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Figure 13. Flowline Flaw Growth - 6x48mm Depth vs. Time
Table 6. Flowline Life Summary
Flaw
Depth
(mm)
Flaw
Width
(mm)
Loading CTOD
(mm)
Parent
Metal
Life
(yrs)
Weld
Life
(yrs)
3 24
0.2% Strain 0.5
211 167
4 32 188 147
5 40 172 130
6 48 159 116
7 56 149 104
8 64 140 94
3 24
0.5% Strain 0.5
197 160
4 32 172 137
5 40 152 119
6 48 137 105
7 56 124 94
8 64 113 83
3 24
0.2% Strain 0.25
211 152
4 32 188 131
5 40 172 114
6 48 159 101
7 56 149 91
8 64 139 60
3 24
0.5% Strain 0.25
181 122
4 32 156 100
5 40 135 83
6 48 119 20
Flaw
Depth
(mm)
Flaw
Width
(mm)
Loading CTOD
(mm)
Parent
Metal
Life
(yrs)
Weld
Life
(yrs)
7 56 106 0
8 64 95 0
CONCLUSIONS
This study evaluated the damage tolerance of a riser and flowline using
limit state and allowable stress as design criteria. It was found that both
the loading histogram and end-of-life load can affect the damage
tolerance of the subsea component.
In some of the cases examined, the higher loads associated with the
limit load design had little effect on the allowable initial flaws. This
was the case for 3 of the 4 riser scenarios examined. Only when the
weld metal was considered with low toughness (Figure 7) was the
damage tolerance, as measured by the size of the allowable initial flaw,
significantly different than that observed with the limit load design.
When the flowlines are assessed, the higher loading associated with the
limit load design affected the damage tolerance of the base metal
significantl , but did not affect the weld metal’s damage tolerance
It is fair to conclude based on these examples that before opting to
allow the higher strains permitted by the limit state design criteria, it is
prudent to investigate the impact of those higher strains on the s stem’s
tolerance to damage.
REFERENCES
Akhtar W, Cerkovnik M, Effect of Crack Face Loading on Reference
Stress for High Pressure Risers and Flowlines, ISOPE 2013.
American Petroleum Institute / The American Society of Mechanical
Engineers (2007). Fitness-For- Service. API 579-1/ASME FFS-1, 2nd
Edition.
API-RP-2RD, Design of Risers for Floating Production Systems (FPSs)
and Tension-Leg Platforms (TLPs), 2009.
British Standard 7910 (2007), Guide on methods for assessing the
acceptability of flaws in fusion welded structures; BS7910.
DNV-OS-F101- Submarine Pipeline Systems, October 2010.
Neuber, H., Theory of Stress Concentration for Shear Strained
Prismatical Bodies with Arbitrary Non Linear Stress Strain Law, J.
Appl. Mech. Dec. 1961, pp. 544-550.
PRCI, Second Generation Models for Strain-Based Design, July 2011
Urthaler Y, et al., An Investigation of the Tolerance of Riser Fatigue to
Corrosion Pitting, OMAE2013-11015.
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