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1 Copyright © 2012 by ASME
PROBABILISTIC MODELS OF RELIABILITY OF CAST AUSTENITIC STAINLESS STEEL PIPING
Haiyang Qian Structural Integrity Associates, Inc.
San Jose, CA 95138 Email:hqian@structint.com
David Harris Structural Integrity Associates, Inc.
San Jose, CA 95138 Email: dharris@structint.com
Timothy J. Griesbach* Structural Integrity Associates, Inc.
San Jose, CA 95138 Email: tgriesbach@structint.com
ABSTRACT The concern of toughness reduction due to thermal
embrittlement of cast austenitic stainless steel (CASS) piping is
increasing as nuclear power plants age. Because of the large
and variable grain size of the CASS materials, the ultrasonic
inspection (UT) difficulties of the CASS components increases
concerns regarding their reliability. Another added concern is
the presence of potential defects introduced during the casting
fabrication process. The possible presence of defects and
difficulty of inspection complicate the development of programs
to manage the risk contributed by these potentially degraded
components.
Experiments have been performed in the past to evaluate
the effect of thermal embrittlement on tensile properties and
fracture toughness as functions of time, temperature,
composition, and delta ferrite content, but considerable scatter
has been shown in the results among the important variables. A
probabilistic approach is proposed for the evaluation of the
aging effect based on the scatter in material correlations,
difficulty of inspection and presence of initial defects. The
purpose of this study is to describe a probabilistic fracture
mechanics analysis approach for the determination of the
maximum allowable flaw sizes in CASS piping components in
commercial power reactors, using Monte Carlo simulation.
Attention is focused on fully embrittled CF8M material, and the
probability of failure for a given crack size, load and
composition is predicted considering scatter in tensile
properties and fracture toughness (fracture toughness is
expressed as a crack growth resistance relation in terms of J-
Δa). The correlation between the reduced toughness and
increased tensile properties due to thermal embrittlement is also
included in the analysis. This paper presents results for CF8M
to demonstrate the sensitivity of key input variables on the most
severely embrittled material. The output of this study is the flaw
size (length and depth) that will fail with a given probability as
a function of load and geometry.
NOMENCLATURE σ = stress
ε = strain
E = elastic modulus
σys = yield stress
σflo = flow stress
α, n = Ramberg-Osgood parameters
JR = material crack growth resistance
Δa = crack extension length
Cv = Charpy impact energy
Cv50 = median value of Charpy impact energy distribution
INTRODUCTION Prolonged exposure of cast austenitic stainless steels
(CASS) to reactor coolant operating temperatures has been
shown to lead to some degree of thermal aging embrittlement
[1, 2]. The relevant aging effect is a reduction in the fracture
toughness of the material as a function of time. The magnitude
of the reduction depends upon the type of casting method, the
Proceedings of the ASME 2012 Pressure Vessels & Piping Conference PVP2012
July 15-19, 2012, Toronto, Ontario, CANADA
PVP2012-78710
2 Copyright © 2012 by ASME
material chemistry, and the duration of exposure at operating
temperatures conducive to the embrittlement process. Static
castings are more susceptible than centrifugal castings, high-
molybdenum-content castings are more susceptible than low-
molybdenum-content castings, high-delta-ferrite castings are
more susceptible than low-delta-ferrite castings, and operating
temperatures of the order of 320°C (610°F) increase the
embrittlement rate relative to the rate at operating temperatures
of the order of 285°C (550°F). The extensive amount of
fracture toughness data available for thermally-aged CASS
materials enables delta ferrite, molybdenum content, casting
type, and service temperature history to be used as the bases for
screening and evaluating components for continued operation
during the license renewal term. Additional information
regarding residual flaws in CASS piping may provide further
insight into the likelihood, or probability, that flaws in piping
systems could become critical in size to challenge the structural
integrity of the component. Griesbach et al. have studied the
flaw tolerance of CASS piping materials using a deterministic
approach [3]. The research shows that the conservatism in
inputs and safety factors greatly reduce the critical flaw sizes of
the CASS piping components. Rather than using a
deterministic approach with conservative inputs, Qian et al.
have used a probabilistic approach that accounts for the large
amount of variability in materials and scatter in the correlations
used to predict the thermal embrittlement [4]. Such an
approach bypasses the need for conservative bounding values,
and takes the scatter explicitly into account. The outcome of
the analysis is the probability of failure (a component of risk)
for a given crack size, rather than conservative estimates of
allowable crack sizes with large safety margins. When
combined with the probability of a crack of a given size being
present and the probability of detecting a crack as a function of
its size, the overall failure probability can be evaluated and the
benefits of inspection determined. Probabilistic fracture
mechanics lends itself to the analysis of systems where
variability and uncertainties on the key parameters can be dealt
with explicitly to calculate an overall probability of fracture
based on maintaining a safety goal. However, the work is based
on a fracture model with tensile stress only and the results are
preliminary. In this study, a fracture model combining tensile
and bending loading based on maximum strain in the piping
component is applied. The correlation between changes in
material toughness and tensile properties are also investigated
as well as the effect of lack of data. This approach offers the
possibility to develop inservice inspection flaw acceptance
criteria for CASS components similar to ASME Code Section
XI, Subsection IWB 3500 and 3600 for austenitic piping or
dissimilar metal welds. This study develops a probabilistic
fracture method for analyzing CASS piping materials and
presents sample results performed for primary system piping in
a PWR.
DETERMINISTIC BASIS The probabilistic analysis is based on a deterministic
fracture mechanics model, with some of the inputs treated as
random variables and Monte Carlo simulation used to generate
results. A circumferential crack in a pipe subjected to axial
loads is considered, as shown in Figure 1.
Elastic-plastic material is considered, with a Ramberg-
Osgood representation of the stress strain curve, as presented in
Equation (1) n
flo
flo
EE
(1)
Figure 1. Part-Through Part-Circumferential Crack in a Pipe
The J-integral is used to describe the crack driving force,
and the applied value of the J-integral is evaluated from the
elastic and fully-plastic J-solutions using the estimation
procedure outlined in Reference [6], which is also described in
Reference [9]. The total elastic-plastic J-integral can be written
as the sum of the elastic and fully-plastic solutions,
pe JJJ (2)
The elastic J-integral can be obtained from stress intensity
factor as
EKJ e
22 1
(3)
The stress intensity factors of tension and bending can be
calculated separately and the superposition of the two solutions
can be added and translated into the elastic J-integral using
Equation (3).
No fully-plastic J-solutions for tension and bending for a
part-through part-circumferential crack are currently available.
Information for tension or bending is available, such as from
References [5, 7 and 8], but most often only for a very limited
range of crack sizes. Due to lack of more complete
3 Copyright © 2012 by ASME
information, the following extrapolation procedure was devised
to estimate fully-plastic J.
The beginning point is to consider the plastic strain on the
cross-section when no crack is present, which is expressed by
Equation (4)
yy o )( (4)
where y is the distance from the center of the pipe. This
relation is the standard assumption of plane cross-sections
remaining plane.
The plastic strain – stress relation is written as n
D
, where
111
1
nflo
n
nED
(5)
This is the standard Ramberg-Osgood relation with only the
plastic strain.
The following dimensionless parameters to define the
loading are defined
mPR
M ;
mo
oo
R
max
;
mPRM
M
1 (6)
where P is tensile force and M is bending moment.
Using the stress-strain relation and integrating over the
cross-section provides the following useful relations.
2
0
/1
/1
max
sin)1(sin)1(),(~
dDhR
PnP
n
n
m (7)
2
0
/1
/1
max
2sinsin)1(sin)1(),(
~d
DhR
MnM
n
n
m
(8)
The function δ is defined as
01
01)(
x
xx (9)
Combining Equations [6, 7 and 8] shows that the following
relation also holds
),(~
),(~
),(~
),(nPnM
nMn
(10)
The integrals in Equations (7) and (8) can be evaluated in
closed form when μ is 0 and 1 (pure bending or pure tension).
Relations for the fully plastic J for pure tension and pure
bending are provided by Cho [7]. The intermediate functions T
and B are employed.
)22(42
)sin(cos2
1
1
AT (11)
]1)22)(1[()]1)(2(1[2
2
1
A
(12)
ha / (13)
2
1
1
h
RR
h
mo
(14)
sin2
1
2
1cos
B (15)
(2-12) The following expression for the fully-plastic J with
combined tension and bending is employed here. M is the
applied bending moment and P is the applied tension force
(which includes the pressure induced axial stress). 1
22
2212
4442
1),,,()1(
1
n
mmm
n
p
hTR
P
hBR
M
hBR
Mnha
DJ
(16)
This can be written in dimensionless form as follows 1
22
1)/1(1
max
~
4
~
4
~
2
1),,,()1(
n
n
p
T
P
B
M
B
Mnh
aD
J
(17)
Equation (16) reduces to the corresponding expressions in Cho
[7] for pure tension and pure bending.
The function h1 plays a big role in Equations (16) and (17),
and the fully-plastic J-solution consists of a table of this
function as a function of crack size (α and θ), mixture of tension
and bending (ζ) and strain hardening exponent (n). As
mentioned above, tabulated values of h1 are very sparse.
Of the available solutions [5, 7 and 8], the widest range of
crack sizes is given by Zahoor [5], but only for Rm/h of 10, and
the Reference [7] bending results are very limited. Due to the
strong need for a wide range of crack sizes (and a lesser need
for a range of Rm/h), the Zahoor tension solution is employed
here, along with the assumption that the dimensionless J p of
Equation 17 for combined tension and bending is the same as
for pure tension. This allows the tension and bending values of
h1 to be estimated from only the tension solution.
Noting that for pure tension (ζ=0), 2~P and 0
~M , the
following relation between the h1 for tension and combined
loading is obtained by use of Equation (17)
1
22
11),(
),(~
),(4
),(~
),(4
),(~
2
),(),,,(),0,,(
n
T
nP
B
nM
B
nMTnhnh
(18)
The values of h1(α,θ,0,n) are for tension, and are obtained
from Zahoor [5]. Equation (18) then allows the values of
h1(α,θ,ζ,n) to be evaluated.
4 Copyright © 2012 by ASME
nR aCJ (19)
The failure criteria are that crack instability occurs at a
crack size (or load) where the applied value of J and dJ/da are
both higher than the values from the crack growth resistance
curve (Equation 19). This is referred to a tearing instability [3,
11, 12]. Failure is instability of a part-through crack to become
a through-wall crack when the flaw depth is deeper than this
calculated critical value.
PROBABALISTIC MODEL
The deterministic model briefly described in the previous
section provides the basis of the probabilistic model. Rather
than using a deterministic approach with conservative inputs, a
probabilistic approach is used that accounts for the large
amount of variability in materials and scatter in the correlations
used to predict the thermal embrittlement. Such an approach
bypasses the need for conservative bounding values, and takes
the scatter explicitly into account. The outcome of the analysis
is the probability of failure (a component of risk) for a given
crack size, rather than conservative estimates of allowable crack
sizes with large safety margins. Similar analyses of piping
reliability have been performed, such as by the PRAISE code
[10]. PRAISE considers similar problems of piping reliability
due to the growth and instability of initial cracks in pipes, but
does not account for time-dependent material degradation.
Furthermore, PRAISE considers tensile properties and material
toughness to be deterministically defined.
The crack growth resistance curve for cast austenitic
materials is subject to a lot of scatter, even for a given
composition, temperature and delta ferrite content [1]. The
toughness decreases with time, going from an unaged condition
to a fully embrittled condition (saturated) in a time depending
on temperature and composition. For typical reactor operating
conditions the fully saturated condition is reached in about five
years (~ 40,000 hours). This transition is not treated here, and
this analysis considers only unaged and fully saturated
conditions. CF8M material is considered, because its behavior
is the poorest among the cast austenitic materials commonly
used in commercial nuclear power plants [1]. The tensile
strength increases and ductility decreases with aging [2].
Reference 4 presents preliminary results for CF8M to
demonstrate the sensitivity of key input variables assuming all
applied stresses to be tensile. Figure 2 summarizes the
probabilistic model for obtaining the sizes of cracks that have a
given failure probability. As depicted in Figure 2, the following
material-related random variables are considered in Reference
4:
initial Charpy impact energy
initial flow strength
ratio of fully aged flow strength to unaged flow strength
material susceptibility, as expressed by the parameter Φ
5/)4.0()( 2 NCMnSiNic (3)
fully saturated Charpy impact energy (for a given Φ ).
In this study, the J-integral solution combining tension and
bending is applied to the case discussed in Reference 4 to
reduce the extra conservatism and obtain more realistic failure
probabilities. Experiments show that the thermal aging
decreases the CASS toughness and increases the tensile
properties [1, 2]. The correlation between the changes in
material toughness and tensile properties, which is represented
by the relation between the Charpy impact energy (Cvsat) and
flow strength (σflo), is considered. A treatment of uncertainty
due to the limited data of such correlation is provided, which is
preliminary and could change as more rigorous approaches are
applied. The scatter in the relation between CVsat and σflo can be
due to inherent randomness (aleatoric) and lack of data
(epistemic). Hence, the probabilistic model to consider such
randomness is modified and presented in Figure 3.
Figure 2. Depiction of Procedures for Evaluating Crack Sizes for a
Given Failure Probability without Considering Correlation
between Changes in Toughness and Tensile Properties
5 Copyright © 2012 by ASME
Figure 3. Depiction of Procedures for Evaluating Crack Sizes for a
Given Failure Probability Considering Correlation between
Changes in Toughness and Tensile Properties
The distributions of these random variables, and the data
upon which the distributions are based, are drawn from
References 1 and 2. Other material related properties are
derived from the above random variables and shown as below.
A. Stress-strain relation: m
flo
flo
EE
, (the unit for stresses is ksi)
Where
312
1
ccc
flo
c1 = 0.008848
c2 = 0.64778
c3 = 0.08077
m=6.6
B. Unaged Material
B.1 Tensile Properties
Yield stress, psi:
mean: 26471
standard deviation: 2917
B.2 Fracture Properties
nV
n aCJ 41.0)()4.25(404
)(log06.0244.0 10 VCn
2
502
ln2
1
2
1)(
V
V
C
C
V
V eC
Cp
CV50 = 130.3 ft-lb
μ = 0.279
C. Saturated Material
C.1 Fracture Properties
nV
n aCJ 41.0)()4.25(404
)(log06.0244.0 10 VCn 041.012.2871.0log eCVsat
For materials with fix chemical compositions:
5/)4.0()( 2 NCMnSiNic
For materials with unknown chemical compositions:
Φmean = 32.711
Φstandard_deviation = 8.905
C.2 Tensile Properties
I. Not considering correlation between toughness and
tensile properties:
Flow stress ratio to unaged materials:
mean: 1.189
standard deviation: 0.071
Yield stress, psi: m
flo
fys
E/1
002.0
II. Considering correlation between toughness and
tensile properties:
σflo=β0+β1Cvsat
Yield stress, psi: m
flo
floys
E/1
002.0
6 Copyright © 2012 by ASME
Not considering lack of data
β0=63.284; β1=-0.283
εmn = 0; εsd = 2.965
Considering lack of data
β0, mean=63.284, β0, std.dev.=3.239
β1,mean=-0.274, β1, std.dev.=0.091
ρ=-0.872
εmn = 0
εsd, mean = 2.965; εsd,std.dev. = 2.28
The loads in the model can be random or deterministically
defined. Similarly, the value of the degradation parameter can
be defined, or the distribution defined from a number of plants
can be used. If the loads and inputs for a specific location in a
specific plant are known, then results can be generated for that
specific location. Alternatively, load and Φ distributions
representative of a fleet of plants can be used to generate failure
probabilities for the fleet of plants.
0
20
40
60
80
100
0 10 20 30 40 50
D:\FortranStuff\CF8MFIG.OUT
10
50
90
roo
m te
mp
era
ture
CV
sa
t, ft
-lb
5/)4.0()( 2 NCMnSiNic
Figure 4. Charpy Energy vs. Chemical Composition, Data of
Figure 6 of NUREG/CR-4513 [1] for CF8M, Ni<10%, along with
median and fitted tenth and ninetieth percentiles
RESULTS Results are presented for an example problem of a part-
circumferential crack in a pipe. The dimension and loading
parameters are representative of a cold leg to pressure vessel
joint. The pipe size is:
Outer Diameter = 32 inches
Thickness = 2.25 inches
The pressure is 2250 psi, which corresponds to a tensile
stress of 8 ksi, with an assumed peak bending moment at
different stress levels.
A. Random Toughness
There are two types of random distributions in terms of
Charpy impact energy as shown in Figure 3. One is the random
distribution of toughness for a fixed chemical composition
(distribution in the vertical direction for a fixed Φ value as
shown in Figure 4). Another is the random distribution of
toughness with respect to the distribution of chemical
compositions (distribution of Φ values in the horizontal
direction as shown in Figure 4). In this section, the only
random variable is the toughness for a fixed chemical
composition. The composition, delta ferrite content and tensile
properties are based on Heat 205 of NUREG/CR-4513 [1],
which are summarized below as the percentage by weight.
Cr = 17.88 Mn = 0.93
Mo = 3.34 C = 0.04
Si = 0.63 δc = 1539
Ni = 8.80 σys = 29.0 ksi σflo = 57.2 ksi
α = 50.14 m = 6.408
Analyses were run for unaged and fully aged properties at
28 ksi tensile stress, with the results summarized in Table 1 and
plotted in Figure 5. The number of trials in the Monte Carlo
simulation was 5x106.
Table 1. Values of a/h for Various θ/π and Selected Probabilities -
Random Toughness
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
a/h
θ/π
5.E-01
1.E-01
1.E-02
1.E-04
1.E-06
5.E-01
1.E-01
1.E-02
1.E-04
1.E-06
Note: solid lines unaged, dashed lines aged, 28 ksi tension
Figure 5. Critical Crack Sizes at Various Failure Probabilities for
Example Problem with Toughness the Only Random Variable
7 Copyright © 2012 by ASME
B. Random Toughness, Tensile Properties and Alloy Content
The effect of random material properties were further
investigated by randomizing the tensile properties and alloy
content. The distribution of thermally aged and unaged tensile
properties and toughness are drawn from References 1 and 2
and described in the previous section. Analyses were run for
fully aged and unaged properties, with the results summarized
in Table 2, plotted in Figure 6. The number of trials in the
Monte Carlo simulation was 5x106 for all cases. In these cases,
toughness and tensile properties are all randomly sampled.
There is no correlation between the sampled properties.
Table 2. Values of a/h for Various θ/π and Selected Probabilities -
Random Toughness, Tensile Properties and Alloy Content, Various
Stresses
C. Correlated Toughness and Flow Strength with Uncertainty
Results were generated considering correlation between the
room temperature Cvsat and high temperature flow strength, with
consideration of uncertainty due to lack of data as described
previously. Hence, only fully saturated conditions are
considered. Computations were performed with 5x105 aleatoric
trials and 50 epistemic trials. Table 3 summarizes the results,
which include epistemic quantiles of 10-5
, 0.01 and 0.5, as
plotted in Figure 7.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
a/h
θ/π
5.E-01
1.E-01
1.E-02
1.E-04
1.E-06
5.E-01
1.E-01
1.E-02
1.E-04
1.E-06
Note: solid lines unaged, dashed lines aged, 28 ksi tension
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
a/h
θ/π
5.E-01
1.E-01
1.E-02
1.E-04
1.E-06
5.E-01
1.E-01
1.E-02
1.E-04
1.E-06
Note: solid lines unaged, dashed lines aged, 8 ksi tension, 20 ksi bending
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
a/h
θ/π
5.E-01
1.E-01
1.E-02
1.E-04
1.E-06
5.E-01
1.E-01
1.E-02
1.E-04
1.E-06
Note: solid lines unaged, dashed lines aged, 8 ksi tension, 15 ksi bending
Figure 6. Critical Crack Sizes at Various Failure Probabilities
for Example Problem, Random Toughness and Tensile
Properties, Various Loadings
8 Copyright © 2012 by ASME
Table 3. Values of a/h for Various θ/π and Selected Probabilities
Considering Correlation and Uncertainty
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
a/h
θ/π
0.5
0.01
10-5
8 ksi tension, 20 ksi bending
Figure 7. Critical Crack Sizes at Various Failure Probabilities
Considering Correlation and Uncertainty, 10th, 50th and 90th
Epistemic Percentiles Shown
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
a/h
θ/π
0.5
0.01
10-5
8 ksi tension, 15 ksi bending
Figure 8. Critical Crack Sizes at Various Failure Probabilities
Considering Correlation and Uncertainty, 10th, 50th and 90th
Epistemic Percentiles Shown
Run were made considering no uncertainty in the correlation
(εsd = 0), and the results coincided with the median results in
Table 3.
DISCUSSION
The probabilistic fracture mechanics model was exercised
for a number of sample cases to demonstrate the sensitivity of
the results for three probabilistic conditions and various
assumed tension and bending loading conditions. The effect of
random toughness was the primary concern for these analyses
because the variation of strength and toughness in the aged
condition is one of the greatest uncertainties for the CASS
materials. For CF-8M materials with high delta ferrite content,
a bounding deterministic analysis produces very conservative
maximum allowable flaw depths that could overly penalize the
CASS piping materials when evaluating flaw tolerance. The
series of sample cases in Figures 5 through 8 show the benefits
or improvement of not having to assume the worst case (i.e.,
lower bound) toughness. Figure 5 shows the effect of the
distribution of saturated material toughness with known
chemical compositions. It can be seen that, for both aged and
unaged materials, the minimum critical flaw depth is above or
close to 40% of the total wall thickness, even with very long
circumferential flaw length (up to 70% of the total
circumference). Also, the difference of critical flaw depth
between the 0.5 quantile and 10-6
th quantile is not big. The
smallest difference 0.5 quantile and 10-6
th quantile lines could
be as small as 5% of the total wall thickness. The thermal aging
effect based on Figure 5 is not critical. The difference is
between 2% to 9% of the total wall thickness, smaller than the
difference between 0.5 quantile and 10-6
th quantile lines.
Figures 6 and 8 present the critical crack depths for aged
and unaged materials, randomizing toughness, tensile properties
and alloy content, for a given load. Comparing to Figure 5, it
can be noted that the critical flaw depth is still big for both aged
and unaged materials. For the unaged material, the 10-6
th
quantile line of critical flaw depth is above 35% of the total
wall thickness, while for aged material, the 10-6
th quantile line
of critical flaw depth is above 40% of the total wall thickness.
It can also be seen that the difference between 0.5 quantile and
10-6
th quantile lines is bigger. The biggest difference is larger
than 20% for the aged material and 30% for the unaged
material. With more random variables involved in the
simulation, this expanded distribution is expected, since more
random property combinations are generated.
A comparison of correlated and uncorrelated results at low
quantiles is not possible with current results. The correlated
runs were made with a number of trials that did not allow
determination of the 10-6
probability because of the number of
epistemic trials run (50). However, for the case of 8 ksi tension
and 15 ksi bending, a comparison of correlated 10-5
results with
uncorrelated 10-6
results shows these two cases to be very
9 Copyright © 2012 by ASME
nearly identical. (Figure 7 shows the epistemic spread in the 10-
5 results is small.) Since the correlated 10
-5 result closely
corresponds to the 10-6
result, the correlated results are less
favorable. (The same crack size that gives 10-6
failure
probability for uncorrelated gives 10-5
for correlated.)
The spread in the results at low probabilities due to
epistemic uncertainty is small, thereby indicating that more data
to reduce uncertainty is not needed. However, the treatment of
uncertainty is subject to change if more data becomes available
and a more rigorous treatment may be identified.
One important note is that, for the same percentile range,
the aged critical flaw sizes are larger than the unaged ones,
which is against the trend of decreasing toughness for thermal
aging effect. However, it should be noted that, with the
decreasing of toughness, the tensile properties increase. The
median value of yield strength increases from 26.47 ksi to 38.51
ksi. Considering that the applied stress is more than 28 ksi, the
plasticity would be big and change of yield strength might
largely change the J-T solution due to applied stresses. This
effect could counter the effect of decreasing toughness. A
deterministic run was performed for both aged and unaged
material using median values of all the random properties. For
both of the two materials, the deterministic lines are both close
to the 10th quantile lines. The deterministic line for aged
material is also higher than the unaged material, which is
consistent with the results from the Monte Carlo simulation.
Hence, it is important to consider the thermal aging effect on
both toughness and tensile properties for the evaluation of
thermal aging of CASS. However, the improvement in flaw
tolerance for aged materials is not uniformly apparent for all
stress levels. For example, Figure 6 shows that the aged
material is better at high stress levels (dashed lines at higher a/h
at top of figure). At lower stress levels, the trend is not so
consistent. This is because the plastic component of Japplied has
a much greater dependence on the yield strength of the material.
SUMMARY
The output of the probabilistic model is crack sizes (i.e., flaw
depth and circumferential length) that would become unstable
with a given probability when specified loads are applied The
large flaw sizes predicted to have a 10-6
failure probability when
Level A and B service loads are applied suggest that CASS
piping is quite flaw tolerant, and such results should be useful in
development of ASME Code flaw acceptance standards for high
delta ferrite CASS piping materials.
ACKNOWLEDGMENTS
The authors acknowledge Mr. Doug Kull and Mr. Tim Hardin
from EPRI for their guidance and support in completing this
work.
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