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Failure Assessment Diagram Assessments of Large-Scale Cracked Straight Pipes and Elbows

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This paper reports defect assessments of experiments on large-scale straight pipes and elbows using failure assessment diagram (FAD) methods. The pipes and elbows were of various pipe diameters and contained a range of sizes of cracks sharpened by fatigue loading. Solutions in the literature for stress intensity factor and limit load have been evaluated and up-to-date solutions used as inputs to the FAD assessments. The assessed loads for crack initiation are close to those observed experimentally for straight pipes under pure bending. For elbows, the assessed loads using the FAD approach are generally lower than the experimental loads for crack initiation demonstrating conservatism in the FAD approach. The FAD assessments give confidence in the use of the modern stress intensity factor and limit load solutions for practical defect assessments. The paper indicates how constraint modifications to the FAD may be used to improve accuracy.
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Transactions, SMiRT-23
Manchester, United Kingdom - August 10-14, 2015
Division II
FAILURE ASSESSMENT DIAGRAM ASSESSMENTS OF LARGE-SCALE
CRACKED STRAIGHT PIPES AND ELBOWS
R A Ainsworth1, M Gintalas1, M K Sahu2, J Chattopadhyay2 and B K Dutta2
1 The University of Manchester, Pariser Building, Sackville Street, Manchester M13 9PL, UK
2 Reactor Safety Division, Hall-7, Bhabha Atomic Research Centre, Mumbai 400085, India
ABSTRACT
This paper reports defect assessments of experiments on large-scale straight pipes and elbows using
failure assessment diagram (FAD) methods. The pipes and elbows were of various pipe diameters and
contained a range of sizes of cracks sharpened by fatigue loading. Solutions in the literature for stress
intensity factor and limit load have been evaluated and up-to-date solutions used as inputs to the FAD
assessments. The assessed loads for crack initiation are close to those observed experimentally for straight
pipes under pure bending. For elbows, the assessed loads using the FAD approach are generally lower
than the experimental loads for crack initiation demonstrating conservatism in the FAD approach. The
FAD assessments give confidence in the use of the modern stress intensity factor and limit load solutions
for practical defect assessments. The paper indicates how constraint modifications to the FAD may be
used to improve accuracy.
INTRODUCTION
In a wide range of industries, structural integrity assessments of piping components containing defects are
required to demonstrate safe and reliable operation. For example, leak-before-break (LBB) assessments of
primary piping systems of some nuclear power plant assume the presence of cracks and demonstrate that
such cracks lead to detectable leakage before pipe burst. There have been many studies addressing the
defect tolerance of piping components, some addressing the influence of defects on the collapse load,
others addressing fracture using linear and non-linear fracture mechanics. This has led to the inclusion of
procedures for assessment of piping components within more general fracture assessment approaches
such as R6 (2013), BS7910 (2013), API 579 (2007), RSE-M (2010) and others.
There is some large-scale experimental validation of the methods for assessment of piping components.
For example, recently Zhu and Leis (2012) examined the burst pressure prediction of over 100 uncracked
pipes while Bedairi et al. (2012) examined the influence of corrosion defects on fracture. Another study
involved a large number of large-scale tests on straight pipes and elbows of various pipe sizes and crack
configurations subjected to different loading conditions, as summarised by Chattopadhyay et al. (2000),
Chattopadhyay et al. (2005) and assessed recently in Chattopadhyay et al. (2014).
This paper revisits the experimental data on large-scale piping components of Chattopadhyay et al. (2000,
2005). Although these data have been assessed using a number of fracture mechanics approaches as
discussed in Chattopadhyay et al. (2014), recently there have been developments in both stress intensity
factor and limit load solutions for defective straight pipes and elbows (An et al. (2010), Lei (2011), Kim
et al. (2007), Lei et al. (2014), Chattopadhyay et al (2004), Chattopadhyay and Tomar (2006)). This
paper uses these up-to-date solutions in conjunction with selected data from Chattopadhyay et al. (2000)
and Chattopadhyay et al. (2005) to examine the accuracy of codified fracture assessment procedures.
23rd Conference on Structural Mechanics in Reactor Technology
Manchester, United Kingdom - August 10-14, 2015
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EXPERIMENTAL DATA
Six fracture tests were carried out on cracked pipes of SA333 Grade 6 steel under quasi-static monotonic
four-point bending as shown schematically in Figure 1. The geometries of the cracked pipes in terms of
outer diameter, Do, thickness, t, mean radius, Rm, and total crack angle of the circumferential cracks, 2θ,
are given in Table 1. Measurements of inner (IS) and outer span (OS) dimensions are also presented in
Table 1. Values of the total load applied to the pipes, the load-line displacement and crack length/growth
were recorded during each test. Initiation loads,
ex
2.0
F
, were defined at a crack extension of 0.2mm. More
details of the tests are described by Chattopadhyay et al. (2000) and Chattopadhyay et al. (2005).
Table 1: Dimensions of large-scale pipe tests
Test number
Outer diameter
Do [mm]
Thickness
t [mm]
Rm/t
Outer span
OS [mm]
Inner span
IS [mm]
Crack angle
[°]
SPBMTWC8-1
219
15.15
6.73
4000
1480
65.6
SPBMTWC8-2
219
15.10
6.75
4000
1480
93.9
SPBMTWC8-3
219
15.29
6.66
4000
1480
126.4
SPBMTWC16-1
406
32.38
5.77
5820
1480
96.0
SPBMTWC16-2
406
32.15
5.81
5820
1480
126.3
SPBMTWC16-3
406
32.36
5.77
5820
1480
157.8
Eight 90º elbows of SA333 Grade 6 steel with circumferential through-wall cracks, at the intrados or
extrados, were tested by applying static in-plane bending. The elbows cracked at the extrados were tested
under closing mode and those cracked at the intrados were tested under opening mode. Straight pipes
were welded to each side of an elbow and to flanges, bolted to circular plates, for connection to the
loading. Figure 2 is a schematic of an elbow test set up.
The geometric properties of the elbows are given in Table 2 and are similar to those of the straight pipes
but additionally include the bend radius, Rb and the elbow factor, λ, defined by
2
mb R/tR
(1)
Elbows cracked at the intrados have test numbers containing “IN”; elbows cracked at the extrados have
test numbers which contain “EX”. The experimental loading arrangement is given in terms of the
moment arm length, L, shown in Figure 2.
Table 2: Dimensions of large-scale elbow tests
Test
Number
Outer
Diameter
Do [mm]
Thickness
t [mm]
Rm/t
λ
Bend
radius
Rb [mm]
Moment
arm length
L [mm]
Crack
angle
2θ [°]
θ/π
ELTWIN8-1
219
19.1
5.23
0.40
207
825.72
94.96
0.26
ELTWIN8-2
219
18.8
5.32
0.39
207
825.72
125.16
0.35
ELTWIN16-1
406
36.43
5.07
0.65
609
840.22
95.89
0.27
ELTWIN16-2
406
36.85
5.01
0.66
609
840.22
122.79
0.34
ELTWEX8-4
219
19.3
5.17
0.40
207
825.72
98.24
0.27
ELTWEX16-3
406
35.06
5.29
0.62
609
840.22
64.85
0.18
ELTWEX16-4
406
35.7
5.19
0.63
609
840.22
94.11
0.26
ELTWEX16-5
406
37.6
4.90
0.67
609
840.22
124.00
0.34
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Figure 1. (a) Loading configuration for the pipe
test, where outer span (OS) is distance between
the supports and inner span (IS) is distance
between the loading points; (b) cross-sectional
view of a pipe with a through-wall crack
Figure 2. Loading configuration of an elbow under
in plane bending moment: (a) test set up, (b) cross-
sectional view of an elbow with a through-wall
crack at extrados-closing mode, (c) crack at
intrados-opening mode
INPUTS TO FAD ASSESSMENT
Material data from small-scale tests
Materials data have been obtained from standard tensile tests and three-point bend (TPB) specimens for
the SA 333 Grade 6 carbon steel used in the pipe tests. Results are presented in Table 3; the yield stress,
y
, ultimate stress,
u
, and fracture toughness data depend on the outer diameter of the pipe, Do. Ductile
initiation fracture toughness values J0.2 were obtained using stretch zone width (SZW) measurements at a
crack growth of Δa=0.2mm.
Table 3: Properties of SA 333 Grade 6 steel as a function of pipe diameter
D0 [mm]
E [GPa]
ν
σy [MPa]
σu [MPa]
J0.2 [N/mm]
βT
219
203
0.3
288
420
220 from
TPB 8: a/W=0.513
0.096
406
203
0.3
312
459
236 from
TPB 16: a/W=0.453
0.045
For the 219mm pipe diameter, initiation toughness was determined from TPB 8 specimens with a relative
crack depth a/W=0.513 and for the 406mm pipe from TPB 16 specimens with a/W=0.453. Values of a
constraint parameter βT (
)L/(Tyr
where Lr is the R6 load to limit load ratio and T is the elastic T-
stress) were calculated from
432
TW/a9061.5W/a434.11W/a6956.9W/a8784.49893.0
(2)
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Equation (2) is taken from R6 (2013) for S/W=4 and is valid for 0≤a/W≤0.8. Positive values of constraint
parameter indicate that the fracture toughness values of 220 and 236 N/mm correspond to high constraint.
Stress Intensity Factor Solutions
In order to apply FAD methods, it is necessary to evaluate the stress intensity factor,
I
K
. The following
solution for circumferentially through-wall cracked pipes under in-plane bending moment (R6 (2013),
Zahoor (1985)) was used:
aFK bbI
(3)
where the bending stress,
b
, is defined in terms of the bending moment
b
M
as
)tR/(M2
mbb
(4)
The correction function,
b
F
, in Equation (3) is
24.45.1
b/6422.2/5967.4A1F
for
55.0/0
(5)
where
25.0
m25.0t/R125.0A
for
10t/R5 m
(6)
For each pipe the values of the ratios
t/Rm
and
/
are included in Table 1. All the pipes tested are
within the validity limits on
t/Rm
and
/
in Equations (5, 6).
The stress intensity factor for circumferentially through-wall cracked elbows under in-plane bending is
taken from the solution developed by An et al. (2010) which is also in the form of Equations (3, 4).
Values for the function
b
F
in this case are presented in tabular form in An et al. (2010) for particular
elbow sizes as functions of
t/Rm
,
mb R/R
and
/
. Calculated values of
b
F
for the eight elbows are
listed in Table 4.
Table 4: Values of the function
b
F
for a crack at the centre of the elbow
ELTWIN
8-1
ELTWIN
8-2
ELTWIN
16-1
ELTWIN
16-2
ELTWEX
8-4
ELTWEX
16-3
ELTWEX
16-4
ELTWEX
16-5

Fb
1.654
2.247
1.603
2.022
1.097
0.853
1.201
1.625
Limit Load Solutions
For circumferentially through-wall cracked pipes under combined bending moment and internal pressure,
a limit load,
L
M
, is given by Lei et al (2014), which for bending moment only solution simplifies to
2
my
2
mL R/t12/11sin)2/1(/costR4M
(7)
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Division II
The limit moment for circumferentially through-wall cracked elbows under in-plane closing bending is
taken as the product of the limit moment for an un-cracked elbow
Lu
M
and a weakening factor
:
LuLMM
(8)
The solution for a defect free elbow under closing moment was recently developed in Lei (2011):
1 for
22.0
1
1 for
22.0
1
M
M
1
313.1
1
)R/R(12.0028.1
p
L
Lu mb
(9)
where
p
L
M
is the limit moment for the uncracked straight pipe:
y
2
m
p
LtR4M
(10)
and λ is the elbow factor defined in Equation (1).
The weakening factor due to the presence of the crack is (Lei et al. (2014)):
0.1/5.0 for )/1(12.3
5.0/21.0 for )/(1.244.1
21.0/0 for 0.1
3
(11)
The values of the ratio
/
and λ are included in Table 2 for each elbow.
The limit moment solution for circumferentially through-wall cracked elbows under in-plane opening
bending is again taken as the product of the solution for an un-cracked elbow
Lu
M
and a weakening
factor
as in Equation (8). The solution for a defect free elbow under opening moment was again
recently developed by Lei (2011) as:
)(n2502.08908.0M/M p
LLu
for
0.11.0
(12)
where the uncracked straight pipe limit moment is again given by Equation (10). The weakening factor
due to the presence of the crack in this case is (Chattopadhyay et al. (2006)):
)/(8108.1127.1
for
41.0/125.0
(13)
FAD RESULTS
For the 6 straight pipes under pure bending, the predicted initiation loads based on the fracture toughness
values in Table 3 are compared with the experimental initiation loads in Table 5. Also included in Table
5 are the values of
r
L
,
r
K
at the predicted initiation loads. Predicted values of
p2.0
J
which would lead to
23rd Conference on Structural Mechanics in Reactor Technology
Manchester, United Kingdom - August 10-14, 2015
Division II
assessment points being on the FAD at the experimental initiation load are also given. Figure 3 shows the
assessment points (
r
L
,
r
K
) evaluated at the experimental initiation loads plotted on the FAD.
Table 5: Comparison of experimental and predicted initiation loads for pipes
Test Number
Experimental
initiation
load
ex
2.0
F
[kN]
Predicted
initiation
load
p2.0
F
[kN]
d
[%]
βT
p2.0
J
[N/mm]
at
ex
2.0
F
r
L
r
K
r
L
r
K
SPBMTWC8-1
198.2
186.6
-5.84
-0.514
318
0.998
0.675
0.940
0.635
SPBMTWC8-2
155.9
142.6
-8.58
-0.289
365
0.983
0.748
0.899
0.684
SPBMTWC8-3
122.2
104.7
-14.30
-0.105
558
1.037
0.811
0.889
0.695
SPBMTWC16-1
529.2
539.9
2.02
-0.333
221
0.748
0.795
0.763
0.811
SPBMTWC16-2
400.2
397.2
-0.77
-0.176
242
0.761
0.824
0.755
0.818
SPBMTWC16-3
288.8
289.6
0.29
-0.048
234
0.786
0.787
0.789
0.791
TPB 8
-
5.9
-
0.096
-
-
-
1.288
0.256
TPB 16
-
37.3
-
0.045
-
-
-
1.160
0.36
Figure 3. Circumferentially through-wall cracked pipes.
Experimental initiation load points
(Δa=0.2 mm) on FAD
Figure 4. Circumferentially through-wall cracked
elbows. Experimental initiation load points
(Δa=0.2 mm) on FAD
23rd Conference on Structural Mechanics in Reactor Technology
Manchester, United Kingdom - August 10-14, 2015
Division II
It can be seen that that ductile initiation occurs before plastic collapse and that the predicted initiation
loads are close to the experimental loads. Table 5 includes the percentage differences
For the 8 elbows, the predicted ductile initiation loads are compared with the experimental initiation loads
in Table 6. Also included in the table are the values of
r
L
,
r
K
at the experimental and predicted
initiation loads and predicted values of
p2.0
J
which would lead to assessment points being on the FAD at
the experimental initiation loads. Figure 4 shows the assessment points (
r
L
,
r
K
) evaluated at the
experimental initiation loads, plotted on the FAD. It can be seen that the predicted initiation loads
generally exceed the experimental loads, with the percentage differences given in Table 6, and that ductile
initiation occurs before plastic collapse, although often close to
r
L
=1.
Table 6: Comparison of experimental and predicted initiation loads for elbows
Test Number
Experimental
initiation
load
ex
2.0
F
, kN
Predicted
initiation
load
p2.0
F
, kN
d
[%]
βT
Predicted
p2.0
J
[N/mm]
at
ex
2.0
F
r
L
r
K
r
L
r
K
ELTWIN8-1
113.0
114.3
1.14
-0.282
206
0.934
0.622
0.945
0.629
ELTWIN8-2
89.7
80.4
-10.39
-0.075
405
0.987
0.781
0.885
0.700
ELTWIN16-1
647.6
734.6
13.43
-0.339
159
0.678
0.711
0.769
0.807
ELTWIN16-2
594.3
544.8
-8.33
-0.121
314
0.778
0.922
0.713
0.845
ELTWEX8-4
125.0
140.4
12.32
-0.474
107
0.918
0.460
1.032
0.517
ELTWEX16-3
1382.1
1209.3
-12.50
-0.558
440
1.042
0.686
0.968
0.601
ELTWEX16-4
1004.2
927.8
-7.60
-0.513
331
0.881
0.833
0.814
0.769
ELTWEX16-5
748.4
690.1
-7.78
-0.353
306
0.764
0.923
0.705
0.851
Also shown in Figures 3 and 4 are assessment points for the two sizes of three-point-bend specimen at
initiation, based on solutions for limit load and stress intensity factor in R6 (2013). The positions of the
assessment points clearly differ for components and specimens with crack initiation in specimens
occurring close to the collapse load. There are differences between specimens and components because of
the different geometries and different constraint conditions. A transferability approach to address these
differences is considered next.
CONSTRAINT MODIFIED FAD ASSESSMENT
To transfer fracture data from specimens to components, the stress and strain fields at the crack tip in both
specimen and component should be as similar as possible. A method to match the stress and strain fields
100F/)FF(d ex
2.0
ex
2.0
p2.0
(14)
23rd Conference on Structural Mechanics in Reactor Technology
Manchester, United Kingdom - August 10-14, 2015
Division II
at initiation in the pipe and elbow tests with those in specimens is as follows. First, for the component
tests, the parameters Kr, Lr and the predicted fracture toughness
p2.0
J
at the initiation load are known from
application of the failure assessment procedure and results from Table 5 are reproduced in Table 7 for one
sample pipe tests. From recent finite element results (Gintalas and Ainsworth (2015)), values of βT were
evaluated for cracked pipes under bending and the solution for the sample test is given in Table 7.
Table 7: Transferability parameters for SPBMTWC8-2 pipe and SENT specimen
Parameter
SPBMTWC8-2
SENT Specimen
Step 1
Step 2
Step 3
Step 4
a/W
-
0.5375
0.5375
0.5375
0.5375
a [mm]
-
10.75
18.8125
26.875
33.916
W [mm]
-
20
35
50
63.1
B [mm]
-
5
5
5
5
T
-0.289
-0.289
-0.289
-0.289
-0.289
r
L
0.983
0.983
0.983
0.983
0.983
T
[MPa]
-81.9
-81.9
-81.9
-81.9
-81.9
r
K
0.748
0.421
0.557
0.666
0.748
2.0
J
[N/mm]
365.1
115.7
202.5
289.3
365.1
A test specimen geometry of arbitrary thickness (=5mm here) is then selected. To illustrate the approach,
a long single edge notched tension (SENT) specimen under fixed grip loading has been chosen to match
the SPBMTWC8-2 pipe test. In practice, a number of low constraint test specimen geometries might be
considered. Values of limit load, stress intensity factor and
T
in SENT specimens can be found in R6
(2013) and depend on a/W; by selecting a/W=0.5375, the value of
T
for the specimen is matched to that
of the cracked pipe. The ratio Kr/Lr in the SENT specimen depends not only on a/W but also on absolute
size. The next step is to choose W (and hence a, since a/W has already been chosen) for the specimen to
match the ratio of Kr/Lr in the component. Table 7 and Figure 5 show how this has been done in four steps
to illustrate the effect of specimen size. An initial choice of W=20mm leads to a ratio of Kr/Lr in the
SENT specimen which is much lower than that in the pipe, similar to the low ratio shown for TPB
specimens in Figure 3. As illustrated in Table 7, increasing W leads to an increase in the ratio of Kr/Lr
and choosing W=63.1 mm, a=33.9 mm for the SENT specimen matches the SPBMTWC8-2 pipe test.
Crack initiation using the FAD is predicted to occur when the line with slope Kr/Lr intersects the failure
assessment curve. Therefore, if initiation in the specimens and components is accurately predicted by the
FAD, i.e. occurs at loads corresponding to points (Kr/Lr ) on the failure assessment curve, then not only
will the ratios of Kr/Lr be the same in components and specimens but also the individual values of Kr and
Lr will be the same. These individual values are listed in Table 7 along with the initiation toughness
corresponding to the value of Kr based on the standard R6 Option 1 failure assessment curve. However,
loss of constraint can be described by defining Kr in terms of a fracture toughness from a high constraint
specimen but using a failure assessment curve which lies outside the Option 1 curve, as set out by
Ainsworth and O’Dowd (1995). If constraint loss is defined in terms of the T-stress, then the
modification to the failure assessment curve depends only on Lr,
T
and material parameters. Thus, since
T
has been chosen to be the same in the SENT specimen and the pipe, the same modified failure
assessment curve applies to both. Therefore, the same assessment principles described above apply and
the individual values of Kr and Lr at crack initiation will be the same in the SENT specimen and pipe, but
23rd Conference on Structural Mechanics in Reactor Technology
Manchester, United Kingdom - August 10-14, 2015
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with a higher value of Kr than that based on the Option 1 curve. This higher value of Kr would be
expected to correspond to a lower toughness closer to the high constraint toughness in Table 3 than the
elevated toughness value in Table 7. There is ongoing work to quantify the material parameters
describing the constraint modified failure assessment curve and hence to quantify this.
Table 7 shows that this transferability approach can be successfully applied using a SENT specimen to
match pipe test SPBMTWC8-2. The defined SENT specimen width, W, fits within the limits of the pipe
cross-section, and it would be possible to cut such a specimen from the pipe wall. However, the approach
is limited by the accuracy of the FAD approach, as the failure assessment point at initiation in the
component may not exactly lie on the FAD, even allowing for constraint loss.
Figure 5. Illustration of the transferability approach plotting Kr and Lr values from Table 7
CONCLUSIONS
This paper has presented assessments of the loads for ductile fracture initiation in 14 large-scale piping
tests; 6 straight pipes and 8 elbows. It has been shown that the use of modern stress intensity factor and
limit load solutions, recently presented in the literature, in conjunction with standard failure assessment
diagram methods, leads to generally accurate assessments of the loads for ductile crack initiation, with a
tendency for some conservatism and greater scatter in elbow tests than in straight pipes under bending.
Applications of constraint based approaches in procedures such as R6 use fracture toughness as a function
of constraint level obtained by testing specimens of different geometry and crack size. An alternative
approach has also been illustrated whereby it has been shown that by selection of specimen geometry (for
example SENT), specimen size, W, and relative crack size, a/W, it is possible in principle to match
constraint levels to those in a specific cracked component.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the assistance of Dr Yuebao Lei, EDF Energy, for provision of his
unpublished work on limit load solutions of defective elbows. Support from the Engineering and Physical
Sciences Research Council (EPSRC) under grant reference EP/K007815/1 is gratefully acknowledged.
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... The Notch Failure Assessment Diagram (NFAD) is frequently used to study the safety and for the fracture assessment of pipelines or elbows with different types of defects [39,41,[63][64][65][66][67][68][69][70][71][72][73][74][75][76]. It depends on the fracture toughness (K C ), defect size, i.e., defect depth ratio (d/t), and the internal loading -pressure (P) [69]. ...
... Numerous previous studies have shown that elbows are more vulnerable than straight pipes due to the more severe stress conditions of elbows with a defect, while assessment points for elbows are typically shifted in comparison with straight pipes and located in the brittle fracture domain of the FAD or NFAD (see subsection 3.3.) [17,52,[63][64][65]. ...
... A schematic representation of a typical NFAD with two characteristic polar angle values ( 1 and  2 ) that defined three typical domains (>  1 -brittle fracture,  1 > >  2 -elasto-plastic fracture, and <  2 -plastic collapse) is shown in Fig. 7. Failure happens if the assessment point (L r , K r ) is above the interpolation -failure curve K r = f (L r ) [84]. More details about polar angles definition, three typical domains, and the application of the NFAD are presented in numerous previously published works [12,39,41,[64][65][66][67][68][69][70][71][72][73][74][75]84,86]. somewhat higher than the critical semi-elliptical relative crack depth ratio (d/t= 0.28) in the pipe elbow obtained in our previous study [12]. ...
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Pipe elbows (bends) are considered critical pressurized components in the piping systems and pipelines due to their stress intensification and the effect of bend curvature. They are prone and hence more exposed to different corrosion failure modes than straight pipes. Late detection of such elbow damages can lead to different dangerous and emergency situations which cause environmental disasters, pollution, substantial consumer losses and a serious threat to human life. A comprehensive safety and reliability assessment of pipe elbows, including usage of prediction models, can provide significant increases in the service life of pipelines. It is well known that the limit pressure is an important parameter to assess the piping integrity. In this paper, the integrity assessment of damaged pipeline elbows made of API 5L X52 steel was done within the framework of numerical modeling using the finite element method (FEM) and finite element analysis (FEA). The evaluation of numerically FEM modeled limit pressure in the corroded elbow containing a rectangular parallelepiped-shaped corrosion defect with rounded corners at the intrados section was done and compared to different codes for calculating limit pressure. Moreover, the area with the corrosion defects with different relative defect depth to wall thickness ratios was FEM modeled at the intrados section of the pipe elbow where the highest hoop stress exists. The results showed that the codes for straight pipes could not be applied for the pipe elbows due to the significantly higher error in the obtained limit pressure value compared with numerically FEM obtained results. However, the results for modified codes, adapted for the pipe elbow case using the Goodall formula for calculation of the hoop stress in pipe elbows with defects are pretty consistent with the numerical FEA results. The notch failure assessment diagram (NFAD) was also used for the straight pipe and pipe bends with different corrosion defect depth ratios, while the obtained critical defect depth ratios further highlighted the criticality of pipe elbows as an essential pipeline component.
... The work presented in this paper aims to develop further an alternative single specimen constraint correction method initially introduced in [30,31]. The approach has the potential to reduce conservatism in both crack initiation and crack propagation toughness measurement procedures. ...
... In this section the simplified constraint correction approach presented in [30,31] is described qualitatively. Section 3 then presents the information required to apply the method for some particular geometries while later sections illustrate the results of applying the approach by 95 comparison with finite element solutions for the geometries addressed in Section 3. ...
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Commonly, fracture toughness tests on deeply cracked specimens are used to assess defects in large-scale components. The paper presents a method for selection of test specimen type, size and crack length in order to obtain fracture toughness estimates relevant to defects in cracked pipes. The method uses available closed-form T-stress, stress intensity factor and limit load solutions to determine the required specimen dimensions. The paper reports elastic–plastic finite element analyses for single edge notched bend (SENB) and single edge notched tension (SENT) specimens and cracked pipes which demonstrate good agreement of the matching approach, although care is needed in selecting the appropriate limit load solution for SENT geometries.
... The assessment points are obtained as a function of the toughness value of the pipe, the flow stress of the pipe, the stress state at the region of interest, the pipe geometry and the crack dimensions. Details on the use of the FAD for assessing of crack like features are discussed in studies in [19,20,21]. Figure 3 shows a representation of the FAD with annotations to indicate the assessment zones. ...
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Hydrocarbon’s transportation is a very significant aspect of the economic where it must be used with much efficacy. Pipelines are used to transport the aggressive fluids with large volumes over great distance. The structural integrity of piping system is very essential in order to guarantee the transportation continue of energy resources from production fields to their locations of exportation. Pipe elbow is a main component in the piping networks which considers as a critical and sensitive tool due to their stress intensification and the effect of bend curvature. They are more exposed to different corrosion failure modes than straight pipes. The aim of this thesis was to investigate the causes of cracks and defects that occur in the critical positions of piping systems. This work was divided in two axes; numerical investigation and inspection analysis. The numerical axis was performed in two sections; (i) effect of semi-elliptical cracks on the degradation of pipe elbow, and (ii) assessment validity of the international mathematical standards on the pipe bends. A rectangular corrosion defect at the intrados section was done and compared to different codes for calculating limit pressure. Moreover, the area with the corrosion cracks and defects with different relative defect depth to wall thickness ratios was FEM modeled at the intrados section of the pipe elbow where the highest hoop stress exists. The second axis was focused on a real case of pipe elbow which occurred to the erosion-corrosion phenomenon. Different inspection methods such as; (i) optical visualization, (ii) scanning electron microscope (SEM), (iii) X-ray diffraction (XRD) and (iv) X-ray fluorescence (XRF) test, were used to discover the main factors which were responsible for this failure. The obtained results proved that the critical position can be located in different zones according to the boundary and additional service conditions. The numerical results proved that the critical position was found at 72° of intrados side based on the value of Von-Mises stress and SIFs. In fact, the critical position could change with the presence of butterfly valve before the elbow. In addition, the increase percentage of Silicon (Si) on the corroded structure explained that the sand particles were responsible to the erosion-corrosion phenomenon.
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The paper presents T-stress solutions developed to characterize constraint levels in large-scale cracked pipes and elbows. Stress intensity factor, KI, solutions for pipes and elbows are normalised by material fracture toughness to define the Kr parameter in fitness-for-service procedures, such as R6. Adding knowledge on levels of T-stress allows more advanced analysis through a normalised constraint parameter βT. The paper presents analyses for 6 pipes and 8 elbows. Values of the normalised constraint parameter βT are calculated for each pipe and elbow at the experimentally measured crack initiation point. Comparison of constraint levels in the pipes and elbows with those in various types of fracture toughness specimen are used to predict the initiation loads using the R6 method and to provide guidelines for transferability.
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A large throughwall circumferential crack in an elbow subjected to in-plane bending moment can significantly reduce its collapse load. Therefore, it is very important to know the collapse moment of an elbow in the presence of a throughwall circumferential crack. The existing closed-form collapse moment equations of throughwall circumferentially cracked elbows are either too conservative or inadequate to correctly quantify the weakening effect due to the presence of the crack, especially for opening mode of bending moment. Therefore, the present study has been carried out to investigate through elastic-plastic finite element analysis the effect of a throughwall circumferential crack on the collapse moment of an elbow under in-plane bending moment. A total of 72 cases of elbows with various sizes of circumferential cracks (20=0-150 deg), different wall thickness (R/t=5-20), different elbow bend radii (R-b/R=2,3) and two different bending modes, namely closing and opening have been considered in the analysis. Elastic-perfectly plastic stress-strain response of material has been assumed. Collapse moments have been evaluated from moment-end rotation curves by twice-elastic slope method. From these results, closed-form expressions have been proposed to evaluate collapse moments of elbows under closing and opening mode of bending moment. The predictions of these proposed equations have been compared with 8 published elbow test data and are found to be within +/- 11 % variation except for one case.
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Closed form stress intensity factor (K//1) expressions are presented for cracks in pipes subjected to a variety of loading conditions. The loadings considered are: 1) axial tension, 2) remotely applied bending moment, and 3) internal pressure. Expressions are presented for circumferential and axial cracks, and include both part-through and through-wall crack geometries. The closed form K//1 expressions are valid for pipe radius to wall thickness ratio between 5 and 20.
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This paper provides tabulated solutions of elastic stress intensity factors and crack opening displacements for circumferential through-wall cracked elbows under internal pressure and under in-plane bending, based on extensive three-dimensional elastic finite element analyses covering a wide range of crack lengths and elbow/pipe geometries. The effect of crack length and elbow/pipe geometry on the results is discussed, with particular emphasis on the crack closure behaviour under in-plane bending.