probabilistic models of reliability of cast austenitic ... models of...probabilistic models of...

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:[email protected]

David Harris Structural Integrity Associates, Inc.

San Jose, CA 95138 Email: [email protected]

Timothy J. Griesbach* Structural Integrity Associates, Inc.

San Jose, CA 95138 Email: [email protected]

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


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


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.


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


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


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


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


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


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


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


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.

REFERENCES 1. O.K. Chopra, Estimation of Fracture Toughness of

Cast Stainless Steels During Thermal Aging in LWR Systems,

U.S. Nuclear Regulatory Commission Report NUREG/CR-

4513, Rev. 1, 1994.

2. W.F. Michaud, P. T. Toben, W. K. Soppet and O. K.

Chopra, Tensile Property Characterization of Thermally Aged

Cast Stainless Steels, U.S. Nuclear Regulatory Commission

Report NUREG/CR-6142, 1994.

3. T. J. Griesbach, V. Marthandam, H. Qian, and P.

O’Regan, Flaw Tolerance Evaluation of CASS Piping

Materials, Proceedings of PVP2009 ASME Pressure Vessels

and Piping Division Conference, July 26-30, 2009, Prague,

Czech Republic, PVP2009-77421, 2009.

4. H. Qian, D. Harris, and T. J. Griesbach, Probabilistic

Models Of Reliability Of Cast Austenitic Stainless Steel Piping,

Proceedings of PVP2011 ASME Pressure Vessels and Piping

Division Conference, July 17-21, 2011, Baltimore, USA,

PVP2011-57270, 2011.

5. A. Zahoor, "Ductile Fracture Handbook," Vol. 2, EPRI

Report NP-6301-D, June 1989.

6. Kumar, V., et al., "An Engineering Approach for

Elastic-Plastic Fracture Analysis," EPRI Report NP-1931, July

1981.

7. D.H. Cho, H.B. Seo, Y.J. Kim, Y.S. Chang, M.J. Jhung

and Y.H. Choi, “Advances in J-integral Estimation of

Circumferentially Surface Cracked Pipes”, Fatigue & Fracture

of Engineering Materials & Structures, to be published, 2011.

8. Y.J. Kim, J.S. Kim, Y.S. Lee and Y.J. Kim, “Non-linear

Fracture Mechanics Analyses of Part Circumferential Surface

Cracked Pipes”, International Journal of Fracture, Vol. 16,

2002, pp. 347-375.

9. T.L. Anderson, "Fracture Mechanics," 2nd Edition,

CRC Press, 1995.

10. D. O. Harris, E. Y. Lim and D. Dedhia, Probability of

Pipe Fracture in the Primary Coolant Loop of a PWR Plant,

Vol. 5: Probabilistic Fracture Mechanics Analysis, U.S. Nuclear

Regulatory Commission Report NUREG/CR-2189, Vol. 5,

Washington, D.C., August 1981.

11. W. H. Bamford and E. I. Landerman, “Thermal Aging

of Cast Stainless Steel, and Its Impact on Piping Integrity”,

Journal of Engineering Materials and Technology, Volume 107,

January 1985.

12. C. Buchalet, Y. Meyzaud, Ph. Taupin, “Effect of Long

Term Aging On The Critical Defect Sizes In Primary Piping

Cast Stainless Steel Elbows”, Proceedings of the Second

International Symposium on Environmental Degradation of

Materials In Nuclear Power Systems-Water Reactors, Monterey,

California, September 9-12, 1985.

probabilistic models of reliability of cast austenitic ... models of...probabilistic models of...

Documents