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Proceedings of the ASME 2015 Pressure Vessels and Piping Conference
PVP2015
July 19-23, 2015, Boston, Massachusetts, USA
PVP2015-45567
UNCERTAINTY CHARACTERIZATION OF THE TWC_FAIL THROUGH-WALL
CIRCUMFERENTIAL CRACK STABILITY MODULE FOR XLPR
Paul Scott
Battelle Memorial Institute
505 King Avenue
Columbus, OH, 43201 USA
Tel: (614)-571-5520
Email: scott-C@battelle.org
Richard Olson
Battelle Memorial Institute
505 King Avenue
Columbus, OH, 43201 USA
Tel: (614)-424-4539
Email: olson@battelle.org
for Leak-Before Break (LBB) relief, the US NRC and EPRI
have been jointly funding the development of a fully
probabilistic analysis software tool, known as xLPR for
eXtremely Low Probability of Rupture, to evaluate the
probability of ruptures in Alloy 82/182 dissimilar metal welds
[1].
Probabilistic pipe fracture analyses are built upon
deterministic models. In xLPR there are models for crack
initiation, crack growth, crack coalescence, crack opening
displacement (COD), leak rate, and crack stability in order to
characterize the crack behavior from when it first appears as a
surface crack (SC), to when it may become a leaking throughwall crack (TWC), to when the through-wall crack finally fails.
Models embedded into xLPR also include crack inspection,
leak detection, and mitigation to deal with the effect on
probability of rupture of actions associated with operation and
maintenance.
Focusing only on crack stability, it is assessed in xLPR for
both surface cracks and leaking through-wall cracks. In either
case, conditions (crack size and load), at some instant of
analysis time, may be large enough to cause an instability
(rupture), so xLPR must include an assessment of whether or
not the current state is stable at each time step. Generally, such
stability assessments are performed using limit-load or elasticplastic fracture mechanics (EPFM) models.
Restricting attention to the circumferential crack case, the
xLPR module for TWC stability is called TWC_Fail.
TWC_Fail evaluates circumferential through-wall crack
stability based on the minimum critical crack size of a
limit-load solution and an EPFM J-estimation scheme.
Although it would be ideal if uncertainty of such a module was
only the consequence of the uncertainty of the input
parameters, these are, after all, only simplified models of very
complex behavior so the model itself has uncertainty. Within
ABSTRACT
The US NRC/EPRI xLPR (eXtremely Low Probability of
Rupture) probabilistic pipe fracture analysis program uses
deterministic modules as the foundation for the calculation of
the probability of pipe leak or rupture as a consequence of
active degradation mechanisms, vibration or seismic loading.
The circumferential through-wall crack stability module,
TWC_Fail, evaluates through-wall circumferential crack
stability based on the minimum crack size from the Net-Section
Collapse or an EPFM J-estimation scheme analysis. Beyond the
uncertainty of xLPR data inputs, each module has an
uncertainty. This paper documents the module uncertainty for
TWC_Fail.
Using 32 pipe fracture experiments, including: base metal,
similar metal weld, and dissimilar metal weld experiments;
bend only and pressure and bend loading; pipe diameters from
2-inch nominal diameter to 42-inch diameter, cracks that range
from short to long, the uncertainty of the TWC_Fail
methodology is characterized. Results show that TWC_Fail
predictions are sensitive to the choice of J-R curve input (J-D or
J-M from C(T) specimen tests) and the fit of the stress-strain
data. Module uncertainty is characterized in terms mean fit and
standard deviation between predictions and experimental
values.
INTRODUCTION
Probabilistic fracture analyses use system input parameters
such as material strength, material toughness, operating
conditions (temperature, pressure, external loads), etc. sampled
many times to determine the probability of some undesirable
event occurring. For nuclear power plant piping, the events of
interest are leaks and ruptures. To address the contemporary
issue of primary water stress-corrosion cracking (PWSCC) in
nuclear piping systems that the US NRC has already approved
1
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the complete context of probabilistic pipe fracture analyses, the
calculated probability of rupture is really a joint probability
involving the uncertainty in the sampled inputs and the
uncertainty of the model(s).
To be able to isolate the effect of the uncertainty of the
xLPR TWC_Fail circumferential crack stability models, a
comparison of TWC_Fail predictions with real-world
experience must be made. Ideally, such a comparison would be
based on operating plant experience. Unfortunately (or
fortunately, really), there have not been any TWC pipe ruptures
in nuclear power plants. Instead, characterization of the
TWC_Fail module uncertainty must rely on data from rather
idealized pipe fracture experiments. Using pipe fracture
experiments including: base metal, similar metal weld, and
dissimilar metal weld experiments; bend only and pressure and
bend loading; cracks that range from short to long, the
uncertainty of the TWC_Fail methodology is characterized and
documented in this paper. The results of this work will be used
to condition the calculated rupture probabilities from xLPR and
will serve as a benchmark for subsequent work in TWC crack
stability.
yes (if_flag = 1) or no (if_flag = 0), as well as the ratio of the
).
known crack angle ( ) to the critical crack angle (
The TWC_Fail module uses a main subroutine TWC_Fail,
for doing the through-wall crack assessment and, presently, two
) prediction methodologies are
TWC critical crack size (
implemented:
• Idealized through-wall crack Net-Section Collapse
(NSC) analysis method [2, 3] and
• LBB.ENG2 elastic-plastic fracture mechanics (EPFM)
though-wall crack J-estimation scheme [4].
In the current version of TWC_Fail, both the idealized
crack NSC and LBB.ENG2 elastic-plastic through-wall crack
predictions are made. Upon return to the calling program, the
solution that yields the smallest critical crack size is used for
the pass/fail assessment and for calculating the ratio of the
current crack size to the critical crack size.
The critical crack size that TWC_Fail predicts is a function
of the pipe geometry, TWC crack size, pipe strength properties,
pipe material fracture toughness, and applied load. The reader
is directed to References 2-4 for details of the theory.
DATA FOR TWC_FAIL UNCERTAINTY ASSESSMENT
TWC_Fail methodology uncertainty was characterized by
comparing the outputs of the module with existing full-scale
experimental pipe fracture data. Over the years, a number of
NRC-sponsored research programs have conducted full-scale
pipe tests. Those programs include:
• The Degraded Piping Program – Phase II [5]
• The First and Second International Piping Integrity
Research Group (IPIRG) programs [6, 7]
• The Short Cracks in Piping and Piping Welds program
[8]
• The Dissimilar Metal Weld Pipe Fracture program [9].
The test specimens for these experiments were sections of
nuclear grade piping of various sizes, materials, loading
conditions, and crack geometries.
• Pipe sizes – 2 to 42-inch nominal diameter, with wall
thicknesses up to 89 mm (3.5 inches).
• Materials – carbon steels (including representative
weld processes), stainless steels (including
representative weld processes), Inconel, and dissimilar
metal welds.
• Loading conditions – simple quasi-static four-point
bending, combined pressure and four-point bending,
dynamic, cyclic, and combined dynamic/cyclic pipe
system experiments.
• Crack geometries – simple through-wall cracked pipe,
part-through surface cracked pipe, and complex
cracked pipe geometries. However, for this validation
exercise, only the simple through-wall cracked pipe
experiments were included in the evaluation matrix.
In total, there were approximately 140 pipe fracture
experiments conducted at Battelle as part of these NRCsponsored research programs [5-9]. In addition, there were a
few early experiments conducted at Battelle as part of an
Electric Power Research Institute program [10]. Included in the
NOMENCLATURE
d-c EP
direct current electric potential drop
DMW
dissimilar metal weld
EPFM
elastic-plastic fracture mechanics
EPRI
Electric Power Research Institute
J-D
deformation J
J-M
modified J
J
Fracture toughness
initiation value of J
J
,
J-R curve fitting coefficients
MP
percent of the stainless steel strength
properties to use in a DMW analysis
NSC
net-section collapse
SC
surface crack
TWC
through-wall crack
US NRC
United States Nuclear Regulatory
Commission
∆
crack extension
,
Ramberg-Osgood equation coefficients
strain
Ramberg-Osgood reference strain
experimental TWC half angle
predicted critical TWC half angle
stress
Ramberg-Osgood reference stress.
TWC_FAIL TECHNICAL BASIS
The TWC_Fail module assesses the stability of a
circumferential through-wall crack (TWC) in a pipe subjected
to combined tension and bending loading. Based on input
pipe/crack geometry, pipe material properties and loads, the
) is
predicted critical crack size of the through-wall crack (
compared with a known current crack size, . A flag is returned
that indicates the result of this comparison: Predicted failure,
2
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overall matrix of pipe fracture experiments, 57 considered
circumferential through-wall cracked pipe subjected to a variety
of loading conditions. Of these 57 circumferential through-wall
cracked pipe experiments, 25 were missing one or more of the
required inputs for the TWC_Fail module so that they were not
considered in the uncertainty assessment for TWC_Fail. That
left 32 experiments to be used in the evaluation of TWC_Fail.
Table A-1 is a summary of the primary characteristics of those
32 experiments.
Material strength properties, Ramberg-Osgood parameters,
consistent with Equation 1 are needed as inputs for TWC_Fail,
as well as fracture toughness (J-R) data consistent with
Equation 2.
(1)
∆
TWC_Fail as part of the Quality Assurance documents for
xLPR.
Both deformation J (J-D) and modified J (J-M)
formulations [11] were fitted to Equation 2, where the data
were available. Typically, data from multiple fracture toughness
specimens were available for analysis. Some specimens were
side grooved while others were not. For some specimens, the
machined notches were fatigue pre-cracked, while for others
they were not. For those cases where there were multiple
specimens of the same geometry, i.e., same side grooves and
same notch acuity, average values of Ji, C, and m for the
multiple specimens were used in the analyses.
Figure 1 shows typical data for a Ramberg-Osgood fit,
while Figure 2 shows a typical J-R curve fit. In both cases, the
fits are very good.
(2)
. For this exercise, the engineering stress-strain data for each
of the individual tensile test specimens for a particular
experiment were fit over the range of 0.1 percent strain to the
strain corresponding to 80-percent of the ultimate strength
using a least squares fit. For those materials for which there
were multiple tensile specimens available, a composite fit of
the ensemble of stress-strain curves was made by minimizing
the error, in a least square sense, between every measured
stress-strain data point and the single best equation for all of the
available tensile specimens.
Prior experience has shown that predictions of TWC
stability for welds are governed by strength properties of the
base metals and toughness of the weld material. For the
dissimilar metal weld (DMW) pipe tests where there are two
base metals, stainless steel and carbon steel, a combination of
the two base metal strength properties was used in the analysis
using Equation 3.
100
100
100
Figure 1. Comparison of actual stress-strain data for tensile
specimens F26-5 and F26-6 with composite fit to RambergOsgood relationship for both specimens
(3)
Per the nomenclature, MP is the percent of the stainless steel
properties to use in the analysis, i.e., 30-percent for the 30/70
Mixture Percentage used for the case where the crack is located
in the butter material. Although “yield” is indicated in Equation
3, the same kind of relationship applies for the ultimate
strength, reference stress, Ramberg-Osgood coefficient α, strain
hardening exponent n, and elastic modulus E. The strength
property mixture equation given in Equation 3 was established
through analysis of 13 DMW experiments and finite element
results and is documented in the Model Validation Report for
Figure 2. Comparison of actual J-R curve data for fracture
toughness specimens F49W-3 and F49W-4 with average fits
to Equation 2 for both J-D and J-M formulations of J
3
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The main uncertainty associated with the experimental data
is the estimate of the crack size at the maximum moment. In
order to obtain this value, it was necessary to estimate the crack
growth up to maximum moment from d-c electric potential
drop (d-c EP) data. For the record, d-c EP data are never
smooth and user interpretation is always needed. Experimental
load-displacement data and pipe geometry are never an issue.
1.1.1.24
1.1.1.26
1.2-1
1.2-7
1.2-8
TWC_FAIL UNCERTAINTY ANALYSIS RESULTS
Tables 1 and 2 show results from the TWC_Fail analyses
of various TWC pipe fracture tests. Looking at these two tables,
we can see that TWC_Fail predictions using the J-M fracture
toughness does a better job, on average, than predictions using
1.20 compared with
J-D toughness curves [ ⁄
⁄
1.49] and that the scatter is less using J-M (Std
dev = 0.35 versus 0.49)
The ⁄
values shown in red font in Table 1 and Table
2 are those values of ⁄
where TWC_Fail predicted a
critical crack angle (
) that was more than a factor of 2
smaller than the crack angle at maximum moment ( ) from the
values fall remarkably
pipe experiment. (None of the ⁄
below 1.0) As can be seen from Table 1, there are 2
value was
experiments (1.1.1.24 and1-8) for which the ⁄
greater than 2.0 for at least one of the JM-R curves used in the
analyses. When using J-D, it can be seen in examining Table 2
that the number of “problematic” experiments increases to five
(1.1.1.21, 1.1.1.23, and 1-9, in addition to 1.1.1.24 and 1-8).
Looking at the two tables, it is apparent that the choice of J-R
curve can have a dramatic impact on the results. For
is 2.47 when using
Experiment 1.1.1.24, the value of ⁄
JM-R curve data from a 20% side-grooved specimen, while it is
only 1.38 when using JM-R curve data for a non-side grooved
specimen. This improvement in the prediction when using the
non-side grooved specimen can be easily explained when
looking at the two J-R curves (20% side grooved versus nonside grooved), see Figure 3, for the material evaluated in this
experiment (F49W). The J-R curves for the non-side grooved
specimens (Fracture Toughness Specimens F49W-5 and F49W6) are almost a factor of 2 higher than the J-R curves for the
side grooved specimens (Fracture Toughness Specimens F49W3 and F49W-4). For the other “problematic” results from Table
1 (Experiment 1-8) the failure mode was Net-Section-Collapse
(NSC). There does not seem to be any significance to this,
particularly because the crack size used for the NSC is the
crack size at maximum moment, so any thought that NSC does
not consider crack growth is moot.
1.2-11
1.2-12
1-8
1-9
4.2-1
4.3-1
4111-2
4111-3
4111-4
4111-5
4131-1
4131-3
4131-5
4131-7
1.1.1.28
4141-1
4141-3
4141-5
EPRI-6T
EPRI-8T
WJ-1
(1)
Table 1. Results of TWC_Fail uncertainty analysis
using J-M fracture toughness data
Expt.
Number
1.1.1.21
1.1.1.23
J-M Specimen
Geometry (1)
20% SG; FC
20% SG; SMN
20% SG; FC
0% SG; FC
Failure
Mode
ENG2
ENG2
ENG2
ENG2
(2)
20% SG; FC
ENG2
0% SG; FC
NSC
0% SG; FC
No Fail
20% SG; SMN
NSC
0% SG; SMN
NSC
20% SG; SMN
ENG2
0% SG; SMN
ENG2
20% SG; SMN
No Fail
0% SG; SMN
No Fail
20% SG; SMN
ENG2
0% SG; SMN
ENG2
20% SG; SMN
ENG2
0% SG; SMN
ENG2
20% SG; FC
NSC
20% SG; FC (2)
NSC
20% SG; FC
ENG2
20% SG; FC (2)
ENG2
20% SG; FC
NSC
20% SG; FC (2)
NSC
20% SG; FC
NSC
20% SG; FC
ENG2
20% SG; SMN
ENG2
0% SG; FC
ENG2
0% SG; SMN
No Fail
3-pt bend; SMN
No Fail
20% SG; FC
ENG2
20% SG; SMN
NSC
0% SG; SMN
NSC
20% SG; FC
ENG2
0% SG; FC
ENG2
0% SG; SMN
ENG2
20% SG; SMN
ENG2
20% SG; SMN
NSC
0% SG; SMN
NSC
20% SG; FC
ENG2
0% SG; FC
No Fail
0% SG; SMN
No Fail
20% SG; SMN
ENG2
20% SG; FC
No Fail
20% SG; SMN
No Fail
0% SG; FC
ENG2
0% SG; SMN
ENG2
0% SG; FC
ENG2
0% SG; SMN
ENG2
0% SG; SMN
ENG2
3-pt bend; SMN
NSC
3-pt bend; SMN
ENG2
20% SG; FC
No Fail
0% SG; FC
No Fail
Average =1.20, Std dev = 0.35
2.47
1.38
0.98
1.18
1.18
1.04
1.01
0.94
0.92
1.07
1.04
1.06
1.03
2.46
2.46
1.26
1.55
1.30
1.30
1.54
1.07
1.13
1.07
0.85
0.97
1.01
1.06
1.06
1.20
1.08
1.12
1.27
1.38
1.38
1.07
0.95
0.99
1.14
0.94
0.94
1.26
1.25
1.09
1.08
1.09
1.02
1.21
0.93
0.93
SG=side groove; SMN=sharp machine notch; FC=fatigue
precracked
Dynamically loaded C(T) specimen; all other specimens loaded
quasi-statically
⁄
1.15
1.38
1.37
1.06
4
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Table 2. Results of TWC_Fail uncertainty analysis
using J-D fracture toughness data
1.1.1.21
1.1.1.23
1.1.1.24
1.1.1.26
1.2-1
1-8
1-9
4.2-1
4.3-1
4111-2
4111-3
4111-4
4131-1
4131-3
4131-5
4131-7
1.1.1.28
4141-1
4141-3
4141-5
EPRI-6T
EPRI-8T
WJ-1
DMW-6
DMW-9
DMW-11
DMW-13
(1)
(2)
J-M Specimen
Geometry (1)
20% SG; FC
20% SG; SMN
20% SG; FC
0% SG; FC
20% SG; FC
0% SG; FC
0% SG; FC
20% SG; SMN
0% SG; SMN
20% SG; FC
20% SG; FC (2)
20% SG; FC
20% SG; FC (2)
20% SG; FC
20% SG; FC (2)
20% SG; FC
20% SG; FC
20% SG; SMN
Failure
Mode
ENG2
ENG2
ENG2
ENG2
ENG2
ENG2
No Fail
ENG2
ENG2
ENG2
ENG2
ENG2
ENG2
NSC
ENG2
ENG2
ENG2
ENG2
No
0% SG; FC
Solution
0% SG; SMN
ENG2
3-pt bend; SMN
ENG2
20% SG; SMN
ENG2
0% SG; SMN
ENG2
20% SG; FC
ENG2
0% SG; FC
ENG2
0% SG; SMN
ENG2
20% SG; SMN
ENG2
20% SG; SMN
ENG2
0% SG; SMN
ENG2
20% SG; FC
ENG2
0% SG; FC
ENG2
0% SG; SMN
ENG2
20% SG; SMN
ENG2
20% SG; FC
No Fail
20% SG; SMN
ENG2
0% SG; FC
ENG2
0% SG; SMN
ENG2
0% SG; FC
ENG2
0% SG; SMN
ENG2
0% SG; SMN
ENG2
3-pt bend; SMN
NSC
3-pt bend; SMN
ENG2
20% SG; FC
No Fail
0% SG; FC
No Fail
20% SG, FC
ENG2
20% SG, FC
No Fail
20% SG, FC
ENG2
20% SG, FC
No Fail
Average =1.49, Std dev = 0.64
⁄
1.83
2.41
2.91
2.17
4.15
1.81
0.98
1.27
1.28
2.71
3.02
1.56
2.09
1.30
1.32
1.79
1.22
1.38
Figure 3. Comparison of J-R curves for weld F49W
between 0% and 20% side-grooves (F49W is weld
material evaluated in Experiment 1.1.1.24)
Considering the distribution of the predictions, Figure 4
data from Table 1. Variation
shows a plot of all of the ⁄
in ⁄
from using different kinds of fracture toughness
specimens are indicated by multiple symbols plotted at the
same abscissa. Aside from the two outliers (1.1.1.24 and 1-8),
all of the points lie within ± one standard deviation of the mean.
Additionally, Figure 4 suggests that it is unlikely that
TWC_Fail will yield a severely non-conservative prediction
1). Confidence interval testing with the data from
( ⁄
⁄
Figure 4 suggests that the
value is 1.34 with a
99-percent confidence that the true value is between 1.2 and
1.48.
N/A
1.20
1.05
1.14
1.12
1.32
1.20
1.25
1.55
1.50
1.52
1.19
1.07
1.11
1.52
0.99
1.01
1.73
1.57
1.23
1.19
1.19
1.02
1.32
0.96
0.93
1.06
0.97
1.01
0.98
3
2.5
2
θ/θcrit
Expt.
Number
1.5
1
0.5
0
0
5
10
15
20
25
30
Unique Experiment in Order of Table 1
Table 1 results
Figure 4. Distribution of ⁄
(J-M fracture toughness)
Realizing that it may not be possible to dictate to the end
user which formulation of J (deformation J (J-D) or modified J
(J-M)) to use in their analysis and that it may not be possible to
specify which fracture toughness specimen geometry to use,
TWC_Fail, on average, underpredicts the actual failure crack
SG=side groove; SMN=sharp machine notch; FC=fatigue
precracked
Dynamically loaded C(T) specimen; all other specimens loaded
quasi-statically
5
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=1.34) with a standard deviation of
size by 34-percent ( ⁄
0.53, considering every result in Tables 1 and 2.
to Leak-Before-Break and In-Service Flaw Acceptance
Criteria, March 1984-January 1989; NUREG/CR-4082,
Vol. 8; March 1989.
6. Wilkowski, G. M., et al; “International Piping Integrity
Research Group (IPIRG) Program”; Program Final Report;
NUREG/CR-6233, Vol. 4; June 1997.
7. Hopper, A., et al; “The Second International Piping
Integrity Research Group (IPIRG-2) Program”; Final
Report, October 1991-April 1996; NUREG/CR-6452;
March 1997.
8. Wilkowski, G. M., et al; “Short Cracks in Piping and
Piping Welds - Seventh Program Report, March 1993December 1994”; NUREG/CR-4599, Vol. 4, No. 1; April
1995.
9. Scott, P., et al; “Dissimilar Metal Weld Fracture Program”;
NRC Job Code 6958; July 2012.
10. Kanninen, M. F., et al; “Mechanical Fracture Predictions
for Sensitized Stainless Steel Piping with Circumferential
Cracks”; EPRI Report NP-192; September 1976.
11. Zhu, X-K and Lam, P-S; “Deformation Versus Modified JIntegral Resistance Curves for Ductile Materials”;
PVP2012-78729; Proceedings of the ASME 2012 PVP
Conference; Toronto; 2012.
DISCUSSION
The uncertainty of the xLPR TWC_Fail module has been
evaluated by comparing the experimental crack angle at
maximum moment from pipe tests with the TWC_Fail
would
predicted critical crack angle. A value of 1.0 for ⁄
indicate that there was perfect agreement between the
TWC_Fail prediction and the experiment. Deviations from this
value of 1.0 represent uncertainty in either the analysis
methodology or the input data, including the uncertainty due to
the choice of J-R curve used in the analysis. Considering that it
may not be possible to specify to the end user which
formulation of J (deformation J (J-D) or modified J (J-M)) to
use in their analysis and that it may not be possible to specify
which specimen geometry to use, TWC_Fail underpredicts the
actual failure crack size on average by 34-percent with a
standard deviation of 0.53. Furthermore, it is unlikely that
TWC_Fail will give a non-conservative prediction.
With respect to the overall xLPR analysis, TWC_Fail
predictions of through-wall crack instability will, on average,
predict that a crack being evaluated at some pressure, moment,
and axial load, will fail before such a failure is actually
observed in an experiment or in a plant. The implication for
xLPR is that TWC rupture probabilities, from a crack stability
perspective, will be conservatively high.
ACKNOWLEDGMENTS
This work was conducted at Battelle Columbus as part of
the NRC’s Piping Integrity Program. The authors would like to
thank the NRC’s Office of Research for their support of this
program. The authors also wish to thank U.S. NRC and EPRI
for their continued development of the xLPR Program.
REFERENCES
1. Rudland, D. and Harrington, C.; “xLPR Pilot Study
Report”; NUREG-2110; U.S. Nuclear Regulatory
Commission; May 2012 [ADAMS ML12145A470].
2. Rahman, S. and Wilkowski, G.; “Net-Section-Collapse
Analysis of Circumferentially Cracked Cylinders - Part I:
Arbitrary-Shaped Cracks and Generalized Equations”;
Engineering Fracture Mechanics; Vol. 61; 1998; pp. 191211.
3. Rahman, S.; “Net-Section-Collapse Analysis of
Circumferentially Cracked Cylinders - Part II: Idealized
Cracks and Closed-Form Equations”; Engineering Fracture
Mechanics; Vol. 61; 1998; pp. 213-230.
4. Brust, F. W., and Gilles, P.; “Approximate Methods for
Fracture Analysis of Tubular Members Subjected to
Combined Tensile and Bending Loads”; ASME, Journal of
Offshore Mechanics and Arctic Engineering; Vol. 116;
November, 1994; pp 221-227.
5. Wilkowski, G. M, et al; “Degraded Piping Program - Phase
II”; Summary of Technical Results and Their Significance
6
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ANNEX A
TWC_FAIL UNCERTAINTY CHARACTERIZATION EXPERIMENTAL DATA EVALUATION MATRIX
Table A-1. Evaluation Matrix for TWC_Fail Module
Loading
Conditions
Outside
Radius,
mm
Wall
Thickness,
mm
Initial
Half
Crack
Length,
radians
Half Crack
Length at
Maximum
Moment,
radians
Experiment
Number
Program(1)
Material
/ Crack
Location
4111-2
DP3-II
CS Base
4-Point Bend
355.60
23.62
1.162
1.304
4111-3
DP3-II
SS Base
4-Point Bend
533.40
7.11
1.162
1.228
4111-4
DP3-II
CS Base
4-Point Bend
533.40
15.88
1.162
1.255
4111-5
DP3-II
SS Weld
4-Point Bend
359.79
30.20
1.162
1.316
4131-5
DP3-II
SS Base
4-Point Bend
79.43
13.94
1.219
1.417
4131-7
DP3-II
CS Base
4-Point Bend
136.53
18.26
1.087
1.172
4141-1
DP3-II
SS Weld
4-Point Bend
84.14
14.27
1.166
1.241
4141-3
DP3-II
SS Weld
4-Point Bend
206.76
26.19
1.153
1.257
4141-5
DP3-II
SS Weld
4-Point Bend
83.88
14.10
1.203
1.270
WJ-1
DP3-II
CS Weld
4-Point Bend
84.14
11.05
0.955
0.984
1.2-1
IPIRG-1
SS Base
4-Point Bend
84.49
13.89
1.194
1.325
1.2-7
IPIRG-1
CS Base
4-Point Bend
83.82
13.97
1.131
1.241
1.2-8
IPIRG-1
CS Base
4-Point Bend
83.72
13.69
1.169
1.243
1.2-11
IPIRG-1
CS Base
4-Point Bend
83.55
13.11
1.169
1.311
1.2-12
IPIRG-1
CS Base
4-Point Bend
83.71
13.77
1.172
1.312
4.2-1
IPIRG-2
CS Base
4-Point Bend
84.14
14.50
0.522
0.740
1.1.1.21
Short Cracks
CS Base
4-Point Bend
355.60
22.68
0.196
0.407
1.1.1.23
Short Cracks
SS Weld
4-Point Bend
355.60
30.23
0.196
0.347
1.1.1.24
Short Cracks
CS Weld
4-Point Bend
306.07
31.34
0.248
0.375
1.1.1.26
Short Cracks
SS Base
4-Point Bend
53.12
8.31
0.767
0.815
4.3-1
IPIRG-2
CS Base
4-Point Bend
381.76
38.18
0.522
0.764
EPRI-6T
EPRI
SS Base
4-Point Bend
30.16
6.02
0.719
0.726
EPRI-8T
EPRI
SS Base
4-Point Bend
206.76
26.19
1.156
1.319
4131-1
DP3-II
SS Base
Pressure +
Bend
83.22
13.41
1.162
1.269
4131-3
DP3-II
CS Base
Pressure +
Bend
137.07
18.69
1.162
1.328
7
Copyright © 2015 by ASME
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Loading
Conditions
Outside
Radius,
mm
Wall
Thickness,
mm
Initial
Half
Crack
Length,
radians
Half Crack
Length at
Maximum
Moment,
radians
Experiment
Number
Program(1)
Material
/ Crack
Location
1-8
IPIRG-2
CS Base
Pressure +
Bend
199.64
26.16
0.377
0.740
1-9
IPIRG-2
CS Base
Pressure +
Bend
84.46
11.18
0.782
0.886
DMW-6
DMW
DMW
4-Point Bend
108.45
21.25
0.636
0.740
DMW-9
DMW
DMW
4-Point Bend
108.97
21.85
1.170
1.229
DMW-11
DMW
DMW
4-Point Bend
108.12
21.2
1.184
1.242
DMW-13
DMW
DMW
4-Point Bend
108.8
22.2
1.181
1.267
1.1.1.28
Short Cracks
DMW
4-Point Bend
463.55
85.85
1.128
1.223
(1) DP3-II – Degraded Piping Program Phase II; IPIRG – International Piping Integrity Research Group program; DMW –
Dissimilar Metal Weld Pipe Fracture program
8
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