ML031550685
| ML031550685 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse  |
| Issue date: | 05/03/2002 |
| From: | Wilkowski G Engineering Mechanics Corp of Columbus |
| To: | Norris W Office of Nuclear Regulatory Research |
| References | |
| FOIA/PA-2003-0018 | |
| Download: ML031550685 (59) | |
Text
ray I i L-45L i 5 t' _
taV"V MCC \r, l S -M From: "Gery Wilkowski" <gwilkows@columbus.rr.com>
To: "Wally Norris" <WEN@nrc.gov>
Date: 5/3/02 11:19AM
Subject:
Davis-Besse head corrosion margin report Wally:
Attached is the .pdf file of our report on the D-B head corrosion. We spent considerable time establishing what we believe to be the "best-estimate failure criterion". We calculated margins of the calculated "failure pressure" to the operating pressure of 1.07 to 1.39. We also took the SIA results and using their failure criterion had bracketed their results. The SIA failure criterion gave calculated "failure pressures" of about 2.2 higher than using our "best-estimate failure criterion".
The preliminary results from ORNL are also cited, but as I discussed (by e-mail) with Paul VVilliams, then may need more elements in the cladding to refine their model.
We also calculated that the additional corrosion to cause failure at the operating pressure would be about 0.9 to 1.8 inches in the longest direction using our "best-estimate failure criterion".
This report contains proprietary information from SIA and Framatome proprietary reports.
We look forward to any comments you may have.
Three original color copies are being sent in the mail.
Regards, Gery Wilkowski
- Note, new cell phone # ** * **
.r9(O Dr. Gery M. Wilkowski, P.E.
President Engineering Mechanics Corporation of Columbus 3518 Riverside Drive Suite 202 Columbus, OH 43221 Phone/Fax (614) 459-3200/6800 www.emc-sq.com
.**+******.*.****.*********************************. . .--
CC: "Bill Shack" <wjshack@anl.gov>, "Ed Hackett" <emhl@nrc.gov>, "Nilesh Chokshi Ph.
D., P.E." <nccl @nrc.gov>, "Rick Wolterman" <Wolterman-Emc2@columbus.rr.com>, "Dave Rudland"
<rudland_EMC2@columbus.rr.com>, "Zhili Feng" <zfeng@columbus.rr.com>, "Yong-Yi (work) Wang"
<wangemc2@columbus.rr.com>, "Richard Bass" <bassbr@ornl.gov>, "Paul Williams"
<williamspt@ornl.gov>
FO~~~~~"
. 0A
2 :Engineering Mechanics Corporation of MAC,. Columbus 3518 Riverside Drive Suite 202 Columbus, Ohio 43221 1 Phone: (614) 459-3200x228 F= (614) 459-6800 E-mail: g4ilkowstcoIurbusrr.com April 30,2002 Mr. Wallace Norris Project Officer U.S. Nuclear Regulatory Commission Research, Mail Stop T-lOEI0 Washington, DC 20555
Dear Mr. Norris:
This report documents our short-term analysis efforts to assess the margins that might have existed for the case of the RPV head corrosion on the Davis-Besse plant.
Please contact me if you have any questions or comnents.
Best Regards, Dr. Gery M. Wilkowski President Engineering Mechanics Corporation of Columbus
Failure Criterion Development and f \A Parametric Finite Element Analyses to Assess Margins i for the Davis-Besse RPV Head Corrosion by G. Wilkowski, R. Wolterman, D. Rudland, and Y.-Y. Wang Engineering Mechanics Corporation of Columbus April 30,2002 to U.S. NRC - RES EXECUTIVTE
SUMMARY
This report estimates the margins that existed for the cladding in the Davis-Besse head vastage case. The margins on the calculated "failure pressure" to the operating pressure were calculated, as well as the It : amount of additional corrosion that had to occur for failure at the normal operating pressure.
The development of the failure criterion is first presented. The "best-estimate failure criterion" was defined as the pressure that produced the equivalent strain under biaxial loading equal to an average critical value through the thickness in the cladding. The basis of the "best-estimate failure criterion" is
( that the equivalent critical strain underbiaxiall oading corregpondsto the ultimate stress in a uniaxial tension test. This resulted in the "critical equivalent strain" being_ .5 errentunder biaxiaLoading rather ihanthe 11.2 percent strain in the uniaxial tensile test at the start of necking. An additional consideration is needed to account for the strain gradient through the cladding thickness. When the critical strain is exceeded, then there is a redistnbution of stresses that is not accounted for inthe finite element analysis.
T6account for this lack of stressredistnbution, it was assumed that failure vould be reachedwhen ihe average strain in the thickness exceeded the critical strain. The best-estimate "failure pressures" gave xrins of 1.07 to 1.39 on the normal operating pressure. This agreed well with estimated results from the SIA analysis when the same failure criterion was used. Preliminary results from ORNL gave a higher calculated failure pressures it lhesame criterion, but further mesh refinement in the clad region is being pursued. The estimated additional corrosion needed to cause failure at the normal operating pressure was 0.9 to 1.8 inches more in the longest dimension wvhen using our "best-estimate failure criterion`.
The "best-estimate failure criterion" developed in this report gives calculated "failure pressures" that are about a factor of 2.2 lower than the failure criterion used in the SIA report.
These results could be affected by: (1)variable thickness (the average thickness was used in the values given above), (2) potential cladding flaws, (3) the failure strain being lower due to void growth under higher triaxial stresses causing a reduction in the ultimate strength, (4) the assumption of failure occurring when the average strain though the thickness exceeds the critical strain, (5) variability in the stress-strain curve (the curve used appeared to be an average not a minimum), and (6) a different thickness gradient along the transition from the clad region to the full head thickness than w'hat was used.
It is recommended that the cladding lo head thickness transition be documented in the metallographic work lo be done oiice the area is cut out from the head.: If a more precise assessment is desired, then'the failure criterion should be explored further.
I
INTRODUCTION In March of 2002, the Davis-Besse nuclear power plant shut down early for an inspection of potential cracks in control-rod nozzles in the reactor pressure vessel head. This inspection was required by the U.S.NRC due to concems of circumferential cracks that had occurred at other nuclear plants that were also manufactured by B&W. During that inspection, several axial cracks were found using an under-the-head UT inspection technique. The insulation on top of the head made the visual inspection of boric acid deposits difficult.
While making a repair of a cracked nozzle by partially machining the tube away so that a new weld could be made at the mid-thickness region of the head, it was found that a significant part of the head around that nozzle had corroded avay. In some regions, the corrosion was completely down to the cladding, so that only the nominal design 3/16" thick cladding was maintaining the pressure in the vessel. (The actual thickness was greater than the nominal thickness.)
The occurrence of this magnitude of corrosion raised considerable concern at the NRC. One aspect that was desired to know was how close the head was to failure. Failure in this case vould have resulted in a rupture of the cladding causing an opening area equal to or less than the clad-only region. This would have constituted a small to medium-break LOCA that could have been mitigated by the emergency core cooling system and containment building to prevent release of the pressurized water to the outside environment. Hence, the objective of this report was to develop a quick assessment of the margin that might have existed To make this quick assessment, a 2-dimensional parametric finite element analysis procedure was developed to allow the NRC to make an assessment of the margins that might have existed for the Davis-Besse corroded head.
Figure I shows a photograph of the corroded area from above the head. This picture shows vhere the 4-inch outside diameter CRDM tube was, and to the left an area where the entire thickness of the head had corroded down to the stainless steel cladding. The nominal design 3/16" thick cladding had held the internal pressure during some significant time period. After significant investigation and daily conference calls on this matter betveen the NRC, Davis-Besse staff, and their consultants, it was determined that the precise geometry of how the cladding-only area transitioned to the head w>as difficult to obtain. Due to the safety significance of this situation, Engineering Mechanics Corporation of Columbus (Emc2 ) was asked to assist the NRC in determining the margins that existed for this case.
Analyses undertaken for the U.S. NRC by Emc2 are presented in this report, as well as comparisons to SIA results and preliminary results from ORNL.
Some of the information used in this report vas proprietary information from Framatome and SIA.
We would also like to than the following for their assistance and input; Prof Mark Tuttle, University of Washington, Prof. Tony Atkins, Reading University - UK, Professor Jwo Pan, University of Michigan, and Dr. Raj Mohan, Rouge Steel.
2
Figure 1 Photograph showing corroded area in Davis-Besse head APPROACH The approach undertaken in this report was to assess the cladding "failure" pressure in the corroded area using 2-dimensional finite element analysis procedures. Existing gas pipeline pipe corrosion failure models exist, but they are typically not very accurate for deep corrosion flaws. 2 A similar limitation exists for flaw assessment criteria in ASME Section XI, i.e., Code Case N-597. The ratio of depth of the corrosion compared to the thickness of the head was about 0.95, which is beyond the validity range of existing corrosion models.
Consequently, the approach in this effort was to conduct a number of axisymmetric finite element analyses that will allow the NRC to bound the failure pressure for the actual case. The analyses undertaken in this report involved large-deformation finite element analyses of a full reactor pressure vessel head vith a single axisymmetric corrosion pit down to the cladding. The diameter of the corroded area and the thickness of the cladding were variables in these analyses.
In this case, the Davis-Besse low-alloy steel head had a thickness of 6 and 13/16 inches (including the cladding) according to FirstEnergy's submittal to NRC Bulletin 2001-01 (Docket Number 50-346). The cladding had a nominal design thickness of 3/16 inch according to the same submittal. The cladding maximum design thickness was 3/8 inch, and the design minimum thickness was 18 inch thick. Davis-Besse staff reported to the NRC staff that the measured cladding thickness in the corroded area had an average thickness of 0.297 inch with a minimum value of 0.24 inch Kiefner, J. F., and Duffy, A. R., "Criteria for Determination the Strength of Corroded Areas of Gas Transmission Lines," presented at 1973 Arnerican Gas Association Transmission Conference. (Technical basis for ASME B3 1G.)
2 D. Stephens and B. Leis, "Development of an Altemative Criterion for Residual Strength of Corrosion Defects in Moderate- t Iigh-Toughness Pipe", Proceedings of 2000 International Pipeline Conference, Vol. 2, pp. 781-792, October 2000.
3
The finite element analyses only determine the pressure-strain relationship. Since the analyses do not include elements that simulate neckin (i.e., Gurson elements in ABAQUS require additional mateniF parameters, e.g., nitial inclusion size and spacing distributions, that are unknown at this time for the cladding material), a failure criterion needs to be established to estimate a failure pressure from the stress analysis. Although it is generally agreed that the failure will be a plastic collapse (or limit-load) of the cladding, the details in selection of the failure criterion are important. Hence, the folloving section discusses the "Failure Criterion" aspects. The next section gives the description of the finite element analyses. The final section gives the critical pressure diagrams for cases of varying the diameter of the corroded area, the thickness, and different "failure criteria", with an assessment of the margins that might have existed for the Davis-Besse cladding. Detailed pressure versus strain plots are given in Appendices A and B.
FAILURE CRITERION A reasonable suggestion is that the "failure criterion" for the cladding in the corroded area involves a limit-load analysis. In the industrial analysis submitted to date-, it vas assumed that failure would occur in the cladding once it reached the true strain that corresponds to the ultimate strength from uniaxial tensile test data of cladding weld metal at 600F.
Two assessments were made of this "failure criterion" assumption. (1) We compared their TP308 stress-strain curve to data from past NRC piping programs where all-weld-metal 308 stress-strain curves were developed, and (2) the assumption that the uniaxial strain at ultimate stress could be used was assessed.
The reason for the second assessment was that biaxial loading might change the equivalent strain at the start of necking, where necking occurs when the limit-load pressure is reached.
Comparison of Framatome Claddine Stress-Strain Curve to Past Data A stress-strain curve for TP308 cladding weld metal was sent from Framatome so that NRC contractors and industiy contractors would be using similar material properties in their analyses. The cladding is a submerged arc weld (flux based rather than inert gas welding). The data was for a uniaxial tensile test, and came from "raw engineering tensile data at 600 F (minimum) from Auclear Systems Materials Handbook, Vol. 1 Design Data, Section 1A, for TP308/IP308L weld." Although not stated, it probably came from a round-bar tensile test.
A significant number of TP308 weld metal tensile tests were also conducted during the various NRC pipe fracture programs. The data in the latest version of the PIFRAC 4 database was for tests only up to 550F, so that these stress-strain curves might be slightly higher than the 600F data. Figure 2 and Figure 3 show comparisons of the Framatome supplied TP308-weld-metal stress-strain curve (at 600F) to the data from the PIFRAC database (at 550F). As can be seen in Figures 2 and 3, the Framatome supplied 600F data is higher than several of the curves from the PIFRAC database, and there are a few specimens with lower strains at ultimate. If the PIFRAC materials were tested at 600F, it is expected that the stress values might be slightly lower than shown in Figures 2 and 3. Hence, the Framatome stress-strain curve data falls closer to the mean value of the PIFRAC data, but is not necessarily a minimum bounding curve.
3SIA Report on "Operability and Root Cause Evaluation of the Damage of the Reactor Pressure Vessel Head at Davis-Besse - Elastic-Plastic Finite Element Stress Analysis of Davis-Besse RPV Head Wastage Cavity," File No.
W-DB-OIQ-301, Project No. W-DB-OIQ, April 2,2002.
4 Ghadiali, N., and Wilkowski, G. M., 'Vacture Mechanics Database for Nuclear Piping Materials (PIFRAC)," in FatigueanidFracture- 1996 - Volume 2, PVP - Vol. 324, July 1996, pp. 77-84.
4
600 500 -_
co400 -_
a-E 300 05 12 200 100 -
0-0.00 0.05 0.10 0.15 0.20 True Strain Figure 2 Comparison of TP308 weld metal uniaxial stress-strain curves (Framatome at 600F, otbers at 550F) 600 I I I Lowest stra at ulma= in; -
500 00 a-In
~~~~~~~~~~~~~~~~~~~~~~~~ I
,300 a,)
2 -O A8W-101 (SAW) 2-200 + t 4 E ABW-102(SAW)
A8ABW-1 03(SAW)
-- A8W-1 04(SAW) 100 O A8W-105(SAW) e ABW-106(SAVV) 4 Framatome Data
. .4. I Il Il 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 True Strain Figure 3 Comparison of TP308 weld metal uniaxial stress-strain curves (Framatome at 600F, others at 550F) 5
Assessment of Strain Limit for "Failure" Criterion In material behavior, plastic instability can be defined as a severe localization of the plastic deformation in the material due to a decrease in cross-sectional area. Many researchers have modeled this behavior, which is a function of the equivalent stresses and strains in the material. Limit-forming diagrarns are frequently used in the automotive and shipbuilding industries to make sure sheets of steel do not locally neck (wrinkle) under the biaxial stresses of forming. Invariably, everyone that was contacted agreed that the equivalent failure strain under biaxial loading would be lower than under uniaxial loading. No precise data found in this short time-period (a literature survey was started, but was not available at the time of this report) for TP308 stainless steel weld metal under biaxial loading.)
The failure that occurs after localized neck-ing can be described in damage mechanics terms. The void formation that occurs in the necked region is a function of the initial inclusion distribution, as vell as the triaxial stress state and the magnitude of plastic strains. For example, biaxial loading may increase the triaxial stress state but decrease the plastic flow when compared to uniaxial loading. Therefore, an understanding of each phenomenon is important when determining the failure under biaxial-loads.
To determine the decrease in the plastic flow due to biaxial loads, a relationship between the stresses and the strains during the biaxial loading needs to be developed. This development is given in the next section. Using this relationship, the plastic strain limit under biaxial loading can be determined.
The decrease in the equivalent stress at the onset of necking, due to the increase in triaxiality of the stress state when going from uniaxial to biaxial loading, is more difficult to quantify. Logically, the triaxial stress state is the larger contributor to the void growth behavior, and may overcome the compensating effects of having the lower plastic strains. There was not sufficient time to explore this aspect, and some test data on the cladding material under biaxial material may be needed to properly assess the "failure criterion", vhether it is used in this analysis or more detailed analyses by ORNL.
For this initial investigation, it was decided that failure would be defined as the equivalent plastic strain under biaxial loading that corresponds to the stress at the onset of necking in a uniaxial test specimen.
Finally, it should be noted that inclusions in flux welds are well known to reduce the ductile fracture toughness due to crack tip void growth. Similarly, necking (void growth) may start earlier in the flux
,weld metal under equal (1:1) biaxial loading because of the inclusion content is higher for a flux weld than an inert gas weld.
Development of a Constitutive Relationship Under 1:1 Biaxial Loads The analysis that follovs is described in Dowling, N.E., MechanicalBehavior ofMaterials, 1st Ed, Prentice Hall, 1993, ISBN 0-13-579046-8, Section 12.3.4.5 For substantial yielding up to ultimate stress levels, assume the total strains can be viewed as the sum of elastic and plastic components:
-Jorat = e + p (1)
The biaxial stress is a plane-stress state, so assume the stress is referenced to the principal stress coordinate system:
5 Input provided by Prof. M. Tuttle of University of Washington.
6
aI ax a2 = ay U3 =a, =0 x = Txz ri =
For convenience, define:
a2 = 61 The elastic strain is given by the Hooke's law for plane stress:
'l [arl - (*2 + a3)]= E ( - V)
E E C2e =EI[0a2 -v(Cl + 3 )= E (l-v) (2)
-'3e = [a73 -v(c1 + 2)]= -E* 1 + A)
E E Where E and v are the elastic values of Young's modulus and Poisson's ratio, respectively.
The plastic strains are given as:
Elp = [al,- 2 ] E)r ( 2 )
1 7 (al+a3) a, 2A-18 C2p =- C2]- Epc 2. )-2 (3)
- ( 2 Ep 63p = E[3 (l22)=E(IA Where Ep is the "plastic modulus", defined by:
E=$ a (4) ep
= the "effective stress" (closely related to the octahedral shear stress) a = the "effective plastic strains" (closely related to the octahedral shear plastic strain)
Also, the above expression assumes that the Poisson ratio relating stress to plastic strains is 1/2, which is true for most metals.
In general:
a = I(a l a2)2 + (a 2 r3)2 + ( 3 al) 2 For the particular case of plane stress (a 2 =al, a3 = 0):
Theeffectivetotltriniseltetteefetietrssndefeciveplstctrinccr(5)
The effective total strain is related to the effective stress and effective plastic strain according to:
7
- a -
= +
This is valid for an state of stress (including biaxial stress states). Various models have been proposed that relate the effective stresses and strains for theparticularcase of a uniaxial state of stress. For the moment, denote the model used to descnbe the uniaxial stress-strain curve as:
e= f ()
(Calculations will be presented below based on the Ramberg-Osgood model, i.e., the function f(a) that will be used below is the one proposed by Ramberg-Osgood).
Solving for the effective plastic strains:
Ep = (f) - E (6)
Combining Equations (1) - (6) gives (after some algebra):
Aa(lI-2v) (2 f(_
E( '.2 l1-I+)
)++-2 (22-1)(7
=E 2 (7) a, (1-2v)(1+1) (1+ .)
C3E *2 21,IV TY -
The functional form of f(a) must now be specified. The Ramberg-Osgood function is:
- - lIn aa E H Where, n = strain hardening exponent" (a material constant)
H = a material constant Using this form in Eq. (7) and simplifying:
.EL(l-} )+ (2-A) 2 j(1 n)I2n]fa1 l C2 = E (t.- V)+ - (8)
E 2 H) 63=-Va1 (1 4 )(1fr -n)2n a]~
8
If the stress state is uniaxial ( = 0 ), then Eq. (8) reduces to:
(ln EH (9) 62=63 - vall E (2) H )
The equivalent strain can be calculated using the distortion energy theory definition:
V(_
(1-2 __ + (62- _3 ) + (3-E )(O (10)
Using the above equations, the material response under uniaxial and biaxial loading can be compared. If it assumed that failure occurs at the same stress level, the decrease in failure strain due to the biaxial loading can be determined. The properties supplied by Framatome for the stainless steel TP308 weld metal are as follows:
Test temperature, F 600 0.2% yield strength, ksi 30.9 Ultimate strength, ksi 62.3 Uniform elongation 11.8%
Total elongation (not plotted) 20.6%
Using a Ramberg-Osgood curve fit the constants are as follows:
H = 115ksi n = 0.228 with E = 25,570 ksi v = 0.295 The uniaxial stress-strain relationship is given below:
. . .4 . . .
9
Table I Uniaxial stress-strain curve values from Framatome for TP308 weld metal at 600F True strain True stress, ksi 0 0.00 0.20% 30.96 0.50% 37.24 1.00% 42.83 1.50% 46.48 2.00% 49.25 3.00% 53.45 4.00% 56.64 5.00% 59.25 6.00% 61.47 7.00% 63.41 8.00% 65.14 9.00% 66.70 10.00% 68.13 11.15% 69.65 Using these constants and Equations 8 and 10, an estimate of the uniform equivalent strain up to the same ultimate stress under biaxial loading can be made. Letting X=1 and plotting the equivalent strains, the difference between uniaxial and biaxial loading can be seen in Figure 4. The results indicate that if the ultimate stress is used, the equivalent strain decreases significantly when the mode of loading is biaxial.
tension, i.e., the uniaxial value of 11.15% strain decreases to 5.5% for biaxial loading.
10
80 70 60 40 40 2'
2 30 30- 6 -
wExperment na-a F J ~~~~~~~~~~~~Uniaral 20 - Biadal 10 0 0.02 0.04 0.06 0.08 0.1 0.12 True Strain Figure 4 Comparison of uniaxial and calculated biaxial stress-strain curves for TP308 weld metal at 600F Critical Strain Evaluation from Spherical Shell Analysis The section describes the conditions for maximum load in uniaxial tension and conditions for maximum internal pressure for a thin-walled sphere under internal pressure, as was developed by McClintock 6 .
From the maximum load conditions in this analysis, the critical strain can be determined. Since a thin-walled sphere under pressure loading is close to pure 1: biaxial loading, with equal stress components, this analysis provides additional support to the critical biaxial strain criterion to be used.
The conditions for maximum load in uniaxial tension is given in terms of equivalent plastic strain versus equivalent stress relation, dGe (I1) dcep where oae is the equivalent stress and 4' is the equivalent plastic strain.
Assume the equivalent stress-strain relation follows the following form, ae el (ef) (12) 6 McClintock, F.A. and Argon, A.S., "Mechanical Behavior bf Materials," Addison:Wesley Publishing-Company, ISBN 0-201-04545-1.
11
where -,, and n are fitted parameters.
Applying Eq. (12) to Eq. (11), it may be obtained that the maximum load occurs at eP =n . Therefore, the equivalent stress at the maximum load is 0 ."nI =
- n".
In a thin-walled sphere, the condition for maximum load is, 1.5cr- dae (13) dcep Applying Eq. (12) to Eq. (13), it may be obtained that the maximum pressure occurs at 4 =nI1.5.
Therefore, the equivalent stress at the maximum pressure is aere = * (1 . We have, e l.Sn (14)
Using Eq. (14) and a value of n = 0.228 as previously discussed, it is estimated that uni e = 1.097 CPre aep In other words, the equivalent stress at maximum pressure is 91% of the equivalent stress at the maximum load of a uniaxially loaded specimen. This gives an equivalent strain of 7.0 percent.
Strain Gradient Effects An additional consideration that can be significant is the effect of a strain gradient in the ligament There are three different possibilities. Failure occurs when:
- 1. The entire ligament exceeded the "critical strain" value selected (SIA used this approach with 11.2% strain, i.e., the 11.2% minimum strain criterion), or
- 2. When the average strain in the ligament reached the "critical strain" (Emc2 used this approach with the 5.5% average strain criterion), or
- 3. When any point in the ligament first reached the "critical strain" (i.e., the maximum strain criterion).
These three failure criteria are illustrated in Figure 5, which shows the calculated strain gradients through the thickness of a typical finite element analysis.
- ~ ~ ~~ ~~~~ ;.. ~ . ~~~ ~~~~ ~ ~~~~~~~~~~~-
12
0.25 g 0.20
,.:I 0.05 0.05 Eqisot POwticSlrmalZticol Strain Awne StrainFalhij Criion Delinkl. Close-up of remaining ligament of cladding showing five F,77 ~~~~~~025 t
elements through the thickness 0.20 0.15 Prcssure = P2 r0.10 0.05 I
0.05 I.8 1.8 1.4 1.2 10 0.8 0J 0.4 0.2 0.0 Equhg]&nM PI,lic StraW tical Strn 0.25 Minrn Sin, Palu, C,terionDfilition 0.25 0.,25 e.1 0.20 PrCSSUr - P3 ,
0.15 X.15 0.0 I
4.5 4.0 3.5 3.0 2.5 2.0 1.5 D 0.5 0.0
~~~~~~~~~~~~~~~~C.0 Axisymmetic finite element EquKaleni PbsI: SIinirCrilcal Strain model showing remaining ligament at upper left corner.
Figure 5 Plots typical of tbe strain profile through the thickness of the cladding showing the definitions of the maximum, average, and minimum strain failure criteria based on the equivalent plastic strain through the thickness of the remaining ligament of cladding (Note: P < P2 < P3 )
Using the criteria of the entire ligament reaching the critical necking strain of 11.2% may over predict the failure pressure since it does not account for some of the material thinning due to void growth in the ligament and the redistribution of stresses. Using the criteria of the first point reaching the critical strain may be too conservative. The average strain through the thickness may be a reasonable "best-estimate failure criterion", but using the I1.2%.strain value from the uniaxial test is too high due to the biaxial condition.
13
Consequently in our work we provided the plots using the average strain through the ligament (for both 5.5% or 11.2% strain values), and to assess the differences with the SIA approach we also determined the pressure when the entire ligament exceeded the critical strain values of 5.5% or 11.2% strain.
Critical Strain Location The "critical strain" region could be in the central region of the cladding or along the edge. The support conditions along the edge may highly influence the strain at that location. The precise edge conditions are unknown at this time, so a straight segment transition from the cladding-head interface to the outer surface of the head was assumed, as shown in Figure 5. Note that the recent SIA report showed the critical location was along the edgewhere it was assumed the head thickness was a linear change from the ad-only region to a contour of the head thickness being equal to 75-percent of the design thickness.
This corresponds to a thickness slope of 70 to 78 degrees in the SIA model, whereas in our model the slope varies from 35 to 65 degrees. Hence, the edge effects may be less severe in our model. In fact, in all our analyses with different c1adding and diameters,here thicknesses was a change from the critical Tocation when either the corrosion-hole diameter was larger or the thickness vas smaller. here was a hole diameter to cladding thickness ratio where thes oc-curs.Itis*'co-nded that the edge geometry should be documented when the corroded area is removed from the head and examined in a hot-cell.
Other Considerations in the 'Failure Criterion" In the analyses results presented in this report, the thickness in theladdingw a constant value, rather than using the.variable thickness that occurs in welded cladding. Necking should start in the thinnest region, but the magnitude of the rupture area in the aiia61e Nluiiess case may be less than if the entire cladding had the minimum thickness.
Since the analysis conducted in this evaluation involved an axisymmetric assumption, the effect of an adjacent nozzle was not included. Engineering judgment suggests the nozzle may not be that important to the results, but the more detailed analyses to be done by ORNL may confirm that assumption.
The analysis in this report assumed that the corroded hole was perfectly circular. This of course is not the exact corroded area geometry; however, past corrosion research in the oil and gas industry suggests that there is little effect of the non-primary stress direction on the failure pressure7 . Since the pnmary memi~brane oads are equal in 'sphen6l head, t iclar-hoale geometry is the worst-case assumption for a limit-load analysis. The diameter in our analysis should correspond to the largest meridianal dimension in the actual corroded area.
This analysis did not account for anv weld defects that m lower the "failurepresure". Such defects may give nlse to a local necking region, and it is possible that a smaller leakage area may result if failure occurred at claddjpg flaw.
'D. Stephens and B. Leis, "Development of an Alternative Criterion for Residual Strength of Corrosion Defects in Moderate- o High-Toughness Pipe", Proceedings of 2000 International Pipeline Conference, Vol. 2,pp. 781-792, October 2000.
14
FINITE ELEMENT ANALYSIS PROCEDURES For the Davis-Besse head analysis conducted in this report, the corrosion defect was modeled as an axisymmetric pit at the center of the head. The effects of the irregular shape defect and presence of the control-rod penetrations were not included. The ABAQUS commercial finite element analysis softvare was used with four-noded axisymmetric elements. Figure 6 shows the detailed finite element mesh.
4~~~~~~~~~~~~~~~~~~
_ - ,- X I I I X I Figure 6 Axisymmetric finite element mesh for the Davis-Besse head The dimensions of the Davis-Besse head used in these analyses were taken from detailed drawing supplied wNith the FirstEnergy's submittal to NRC bulletin 2001-01 (DocketNumber50-346). Four or five elements were used through the cladding thickness at the center location and 6 to 7 elements at the transition point from the cladding to the RPV head. The cladding thickness and the diameter of the corrosion hole were defined as variables. Large-strain analyses were conducted assuming incremental plasticity with isotropic hardening in the constitutive relationship. The detailed uniaxial stress-strain curve used for the cladding came from Framatome in response to a request from Emc 2 , ORNL, and the NRC as is described in the previous section. An elastic-plastic stress-strain curve was used for the head material, but the stresses in the head material are generally elastic and have very little effect on the strains in the center of the cladding.
The stress-free temperature was 605F in these calculations. SIA used a stress-free temperature of room temperature, whereas the stress free temperature may be closer to 1,1 OOF (the stress-relief temperature of the head after the cladding is put on). The cladding had a higher coefficient of thernal expansion than the lQw alloy steel head. Hence, using the stress-free temperature of 70F and taking the head to 605F produces a compressive stress in the cladding (SIA approach), our analysis was stress-free, but the real 15
situation would have a small tension stress in the cladding at 605F. The strains corresponding to these thermal expansion stresses, hoNvever, are small compared to the large strains at failure being calculated (about 0.1 percent strain versus the 5.5 to 11.2 percent failure strain criteria). Therefore, the errors from these assumptions are probably small compared to the uncertainties in the failure criterion.
To investigate the effect of large-strain versus small-strain analysis options, finite element runs were made with both options. Figure 7 shows the pressure versus strain results for one of the 15 cases investigated. Interestingly, the pressures were consistently higher for the large-strain analysis than for the small-strain analysis. Typically, the opposite is true, but with this geometry, the bulging of the cladding is perhaps better modeled wvith the large-strain option. Since the large-strain option is the most accurate, it was used for the rest of the analysis results that are presented in this report.
A total of 15 fnite element analyses were conducted to investigate the effects of corrosion defect size and remaining cladding thickness on the failure pressure of the RPV head. Table 2 shows the matrix of the finite element analyses conducted.
Table 2 Matrix of finite element analyses I Corrosion defect diameter (inches) l Thickness (inch) 4.0 5.0 6.0 0.375 (maximum design) X X X 0.297 (average measured in X X X corroded area) 0.240 (minimum measured in X X X corroded area) 0.1 88 (nominal design X X X thickness) .
0.125 (minimum design X X X thickness)
The finite element results wvere analyzed to determine the pressure corresponding to the equivalent plastic strain in the ligament The model idealized the corrosion as a circular region with the remaining cladding layer having a constant thickness. No attempts were made to analyze the precise transition from the cladding layer to the remaining head material at the perimeter of the defect region since that information is not know at this time. Rather, the transition in the wall thickness from the cladding to the full head thickness was made so that it was believed to be somewvhat realistic of a gradual change rather than assuming an instantaneous change in thickness. It is expected that the ORNL 3-D analyses will attempt to model the edge effects in detail wvhen they become available. As a result, for a given loading increment, the maximum plastic strain in the cladding layer occurred at the center of the axisymmetric model used in the analysis in this report. At each loading increment, the maximum, minimum, and average values of the equivalent plastic strain through the ligament were recorded. Figure 7 shows a typical plot of the strain at the center of the cladding versus pressure for the case of a 5-inch diameter defect with a cladding thickness of 0.297 inch. Plots similar to Figure 7 for each of the 15 finite element analyses are given in Appendix A for the large-strain analyses. The small-strain analyses results are given in Appendix B, but were not used further in this report.
The summary plots showvn in the next section show the diameter of the head corrosion versus pressure for a given thickness at strains of either 5.5% or 11.2% using the minimum, maximum, and average strains through the thickness criteria. We believe the 5.5% strain limit as an average value through the thickness may be the best estimate of the actual failure pressures.
16
7000 6000 5000 -____
- o. 4000 23000-2000 -_____
1000 0.00 0.05 0.10 0.15 0.20 0.25 0.3D 0.35 OAO OA5 0.50 Equivalert PlasUc Strain fin/in)
CE (min) small deformaon -- (avg) small defomnabon -c (max) small defonration
- E (mn) large deformation -- £(a%g) large deformaton o c (max) large deformation Figure 7 Plot of equivalent plastic strain at center of cladding versus internal pressure for both small-deformation and large-deformation analyses for a 6-inch diameter corrosion area and a cladding thickness of 0.297 inch RESULTS OF PARAMETRIC STUDY SHOWING "FAILURE PRESSURE" VERSUS CORRODED AREA In order to simplify' the numerous pressure versus strain plots that are given in Appendix A, the pressure as a function of corrosion diameter corresponding to the maximum, the minimum, and the average strain in the cladding layer for both the 5.5% and 11.2% strain levels were determined. Recall that the 5.5%
strain criterion was determined by considering the effect of biaxial loading on the stress-strain curve up to the same uniaxial ultimate stress value. No efforts could be made at tis time to estimate if necking would occur at a lower stress value due to the higher triaxial stress conditions in the actual structure than in a uniaxial tensile test. Experimental data or more detailed analyses are needed to make that determination. Results of the critical strain being reached either in the center of the cladding or at the edge were investigated. First the center cladding location results are given in detail and reduced to the key figure. For the edge location, the detailed plots are given in Appendix A, and only the key figure is given. A comparison of the two plots for determining a calculated "failure pressure" is given afterwards.
17
Results at Center of Clad-only Region The following plots show "failure pressure" versus the diameter of the corroded area for a given thickness of cladding. The "failure pressure" represents the internal pressure corresponding to the equivalent plastic strain in the center of the cladding layer previously described.
Figure 8 through Figure 12 show the diameter of the head corrosion versus "failure pressure" for each of the following five values of cladding thickness;
- 0.375" - maximum design cladding thickness,
- 0.297" - average thickness of the cladding measured by the utility,
- 0.240" - minimum thickness of the cladding measured by the utility,
- 0.188" - average design cladding thickness, and
- 0.125" - minimum design cladding thickness.
Note: the pressure values in the following figures were estimated graphically from the plots given in Appendix A.
1 ooo0
.i... . . .
n- 8000 6000 2 .'--'-"-"-
- ' l o a) 2 U-4000 _ __ __ _ _ _ _ _ _ _ ~~ . .. .. - _ ~ ~
__-_.. ~ ~ _1 e
co 0~
e D_
2000 0
3.0 4.0 5.0 6.0 7.0 Diameter of Head Corosion (inches)
- - (max)=5.5% Ce - (avg)=5.5% - - E(min)=5.5% --- E(ma=11.2% t(-(av)=11.2% -t min)=11.2%
Figure 8 Corrosion diameter versus "failure pressure" for critical strain at center of cladding for cladding thickness of 0.375 inch 18
10000 0.
I co 4000 co 60DDu o2 0-E 0- 2000 0lI i 3.0 4.0 5.0 6.0 7.0 Diameter of Head Corrosion (inches)
- £(max)=5.5% - - (avg)=5.5% - - (rin)=5.5% - (max)=112% i (avg)=112% U (min)=112%
Figure 9 Corrosion diameter versus "failure pressure" for critical strain at center of cladding for cladding thickness of 0.297 inch 10000 8000 0.
2 6000
.5 U-2 4000 a-2000 O 4-3.0 1 4.0 5.0 6.0 7.0 Diameter of Head Corrosion (inches) 0 .- c(rnax)=5.5% - - (avg)=5.5% - - (rrin)=5.5% (max)=11.2% * (avg)=112% --- E(min)=112%
Figure 10 Corrosion diameter versus "failure pressure" for critical strain at center of cladding for cladding thickness of 0.240 inch 19
8000 a 6000 (Ia A
= 4000 P-o,, 40 rE 2000 EL 0~
3.0 4.0 5.0 6.0 7.0 Diameter of Head Corrosion finches)
(max)=5.5% - - (avg)=5.5% - c(nin)=5.5% -+E(maX)-112% A--(avg)=l1.2% - (min)=112%
Figure 11 Corrosion diameter versus "failure pressure" for critical strain at center of cladding for cladding thickness of 0.188 inch 5000 -
4000-w 3000 1000 -
3.0 4.0 5.0 6.0 7.0 Diameter of Head Corrosion (inches)
- - (rma)=5.5% - - (avg)=5.5% - - £(rrin)=5.5% +-(max)=11.2% *-(ag)=1.2% t (min)=11.2%
Figure 12 Corrosion diameterversus "failure pressure" for critical strain at center of cladding for cladding thickness of 0.125 inch 20
Another way to assess this data is to plot the "failure pressure" versus cladding thickness for a given diameter of corrosion. One plot of this type is shown in Figure 13 for illustration purposes.
10000
- z. 8000 co 6000 e'2 ni 4000 e
L0 (L2000 O 4-0.1D 0.15 0.20 0.25 0.30 0.35 0.40 Cladding Thickness (inch) for 5-inch Corrosion Diameter
- -'E - c(MaX)=5.5% - - E
£(aVg)=5.5% - - E(min)=5.5% .-4--E(ma)=11.2% E(aVg)=11.2% -- W-E(in)=112%
Figure 13 Cladding thickness versus "failure pressure" for critical strain at center of cladding for 5-inch diameter corrosion area Values from Figure 9 through Figure 12 have been combined by normalizing the corrosion diameter with respect to the ligament thickness and plotting the results versus "failure pressure" for having the strain in the center of the cladding. Plots of pressure versus D/t are shown in Figure 14 and Figure 15 for the critical strains of 5.5% and 11.2%, respectively. The three different strain gradient criteria are shown in each figure. These figures show that the data from the pressure-versus-diameter plots for each thickness collapse to a single curve for a given failure criterion. The first occurrence curves are believed to give too low of "failure pressure", whereas the average strain curves are believed to give a best estimate of the expected failure pressure. Hence, Figure 14 and Figure 15 can be used to calculate the "failure pressure" for a significant range of corrosion diameters and thicknesses of interest.
Figure 16 shows a comparison of the 5.5% average-failure-strain criterion (Emc 2 best-estimate failure criterion) to the 11.2% minimum-failure-strain criterion (SIA criterion).
21
10000 8000 6000 c.2 4000 U-12C 2000 0
0 0 10 20 30 40 50 60 Corrosion Diameter/Cladding Thickness (D) a (max)=5.5% A c(ag)=5.5% (min)=5.5%
Figure 14 Plot of DJt versus failure pressure for the 5.5% strain criterion in the center of the cladding 12000 r r 10000 + 4 +
a A*
8000 to 6000 E
a iL 4000 E
L 2000 0 -~~~~~~~
0 10 20 30 40 50 60 Corrosion Diameter/Cladding Thickness (Dt)
- £(max)=1 1.8% A E(aVg)=1 1.8% * (min)=1 1.8%
Figure 15 Plot of D/t versus pressure for the 11.2% strain criterion in the center of the cladding 22
12D0 (n2 I
0.
0 10 20 30 40 50 60 Cofrosion DiameterlCladdirg Thickness ()
A5.5% Average StrainCritenon
- 11.2% MirimunStrainCiterton Figure 16 Plot of D/t versus pressure for comparing the 5.5% average failure strain criterion to the 11.2% minimum failure strain criterion at center of cladding Figure 17 shows the ratio of the failure pressures for the 11.2% minimum strain criterion at the center of the cladding (SIA failure criterion) to the 5.5% average strain criterion (Emc2 best-estimate failure criterion) as a function of corrosion diameter to cladding thicess,D7The figure shows that the failure pressure using the 11.2% minimum strain criterion exceeds that of the 5.5% average strain criterion by approximately 60% over the range of D/t investigated.
2o E
1.9 1.5 c S Ft D
1.7 1.6 1.S
- m~~~~~~~~~~~~~~~~~~~~~~~~~~~
E-IP 4w 1A
- o 1.3 -~ I==
0 12 C
1.1 1.0 0 10 20 30 40 50 Ccrrosion Diameter/Cladding Tlickness (DA)
Figure 17 Ratio of the "failure pressures" from 11.2% minimum strain criterion used by SIA to the.Emc2 best-estimate 5.5% average strain criterion as a function of corrosi6n'diameter io cladding thickness (D/t) at center of cladding '
23
Edge Location Results The other critical strain location could be along the edge or perimeter of the hole. This result may be dependant on the geometry of the transition of the cladding thickness to the head thickness. Figure 5 showed the geometry used in our analyses, whereas the edge geometry in the SIA case was a simple linear slope of about 70 to 78 degrees at the critical edge location, and ORNL used a 90 degree thickness transition.
The details of all the edge-location pressure versus strain plots are given in Appendix A. Rather than recreate similar figures to Figures 8 through 16, only a figure similar to Figure 16 is given here to surmarize all the results from the edge-location "failure pressure" versus dimensionless hole geometry (diameter of the hole over the cladding thickness, D/t). These results are shown in Figure 18 for the Emc 2 "best estimate failure criterion" (5.5-percent average strain through thickness) and the failure criterion used in the SIA report (11.2 percent strain exceeded throughout the thickness).
Figure 19 shows a comparison of the center and edge "failure pressures" versus dimensionless hole geometry. Interestingly, there is a transition of the critical location from the center of the cladding to the edge of the cladding when the hole diameter to cladding thickness ratio (D/t) is 12 for the 5.5-percent average strain criterion. For the 11.2-percent minimum strain criterion, the center region had a slightly lower "failure pressure" than the edge location for all D/t values.
12000 10000
- 8000 a-U) 6000 w
L.
^ 4000 E
e 2000 0.
0 0 10 20 30 40 50 60 Corrosion Diameter/Cladding Thickness (Dh)
A 5.5% Average Strain Critenon
- 11.2% Minimum Strain Criterion Figure 18 Plot of D/t versus pressure for comparing the 5.5% average failure strain criterion to the 11.2% minimum failure strain criterion at edge or claddinz 24
16000 14000 ---
12000 -
C10 0 00 - - - - - -- -
a=C 8000- ;i__
6000 2
rn __ __ :_ __ _ _
CL4000 - __
2000 '11 A, -4~~Th 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Corrosion DiameterlCladding Thickness (Dt)
+ Center c(avg)=5.5% - *- Edge t(avg)=5.5% - Center c(min)=1 1.2% - - Edge E(min)=1 12%
Figure 19 Comparison of "failure pressures" versus D/t for center and edge locations Calculated Mar2ins To determine the margins on either the failure pressure or the margin on the hole diameter, it is first necessary to characterize the corrosion area in terms of an equivalent diameter. Figure 20 shovs the remaining thickness measured on the RPV head between Nozzles 3 and 1. These measurements were taken at a spacing of approximately one square inch by Davis-Besse and their contractors. While these were preliminary measurements, the figure shows that the minimum thickness of 0.240 inch was measured at one location. In addition, there is a region between the nozzle openings where the thickness is less than 0.300 inch over an irregular area. The longest continuous segment in which the cladding thickness does not exceed 0.300 inch is approximately 6.7 inches, as shown by the solid line, or 7.6 inches as shown by the dashed line where only one reading was greater than 0.300 inch in Figure 20.
25
6.5 2.6 3.4 .344 NR 3.9 Approx 6.2 6.2 1.2 .344 Location NR NR 11 I _
N 7 6.2 6.2 1.4 NR .346 1.2 6.2 5.9 NR NR .309 . 0 .365 .305 .313 NR 6.0 3.6 3.6 .303 .255 .273 .260 .302 ,99 5.2 3.8 6.6 3.0 .301 .24 .291 .301 .&3 .302 .310 .315 3.6 6.2 .299 0 .311 .8 304 3.6 3.6 3.6 6.4 6.2 .301 .300 0 .300 .300 3.4 3.4 5.8 6.8 6.2 .27 A .340 .350 .360 .370 .370 .303 NR NR .79 .376 J-groo e weld area .380 NR NR .304
. . - A. -
7 Lines represent the longes t Nozzle 11 continuous segments in which Approx the cladding thickness does not Location exceed 0.300 inch. Line lengths from 6.7 to 7.6 inches.
Figure 20 Layout of the remaining thickness measurements between nozzles 3 and 11 of the RPV head 26
Margins on Failure Pressures The fit through the finite element results shown in Figure 19 was used to make a plot of the bounding failure pressure versus hole diameter for a cladding thickness of 0.297 inch. The results are shown in Figure 21 for corrosion defect diameters up to 20 inches. The symbols in Figure 21 indicate were FE results were available. The solid line beyond the symbols is an extrapolated curve-fit equation. A nominal operating pressure of 2,155 psi is also indicated in the figure.
Assuming that the shape of the corrosion defect has less affect on the failure pressure than the largest meridianal dimension (from gas pipeline corrosion experience), then using the approximate meridianal dimensions of 6.7 to 7.6 inches (from Figure 20) gives a "best-estimate failure pressure" range of 3,000 to 2,300 psig, respectively. This gives a margin on the operating pressure of 1.39 to 1.07, respectively.
Both of these failure predictions are for the edge location, where the actual geometry used is not well known at this time.
Using these same dimensions with the minimum-strain failure criterion with 11.2% critical strain (SIA criterion), the calculated failure pressure would be about 6,300 to 5,700 psig, respectively. This gives a margin of 2.92 to 2.65, respectively.
The ratio of the failure pressures from the two criteria is roughly the factor of 2.2. This is greater than the 1.6 value from Figure 17 since the 5.5% strain criterion has the critical location at the edge of the hole not at the center.
Margins on Corrosion Cavity Diameter Another estimate that could be made from Figure 21 is the size of the corrosion area that could cause failure at the normal operating pressure. Using the average strain criterion with 5.5-percent critical strain gives a meridianal length (diameter from Figure 21) of approximately 8.5 inches, or 0.9 to 1.8 inches of additional corrosion length. Using the SIA minimum-strain failure criterion with 11.2-percent strain gives a meridianal length of approximately 23 inches (extrapolated from Figure 21), or 15.3 to 16.3 inches of additional corrosion for failure at the operating pressure.
14 __ ___ _
z12Me/_.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1000 500 O -
0.00 0.05 0.10 0.15 0.20 0.25 0.30 Equvalent Plaslc Strain (Inlin)
-_ average strain tlrough dadd ng -.maximurn strain through dadding -- minimrn strainftough caddng Figure A-29 Equivalent plastic strain versus pressure at the center for corrosion diameter of 6 inches and cladding thickness of 0.125 inch
- )LJw 4500 4000--11 1 3500 '11-9 300-'1 110 E
c 2000 ~
1500 1000 XZ=
A nn . _ _ _ I__ _ _ _ I__ _ _ _ I__ _ _ _ _ _
0.00 0.05 0.10 0.15 0.20 0.25 0.30 EqevanentPlasfc StralnO(rWn)
-- average strain tough daddng -a maxdmurn staintrough daddng -&- minimurn sirain trough dadding Figure A-30 Equivalent plastic strain versus pressure at the edge for corrosion diameter of 6 inches and cladding thickness of 0.125 inch A-15
APPENDIX B Plots of Equivalent Plastic Strain versus Pressure at the Center of the Cladding Area for the Small Deformation Analyses
'--.3 , . t
8000 7000 ,,, ,,,,,
6000 5000 E
a E
tL 4000 I
sUUu I
2000 j
A 1000
. I . I I. I . . I g 0.00 0.05 0.10 0.15 020 025 EqLivalent Plastc Stain (inMn)
-.-average straintrough daddir - madmxir strainthrough claddng _-*-mirdmum stain trough dadding Figure B 1 Equivalent plastic strain versus pressure for corrosion diameter of 4 inches and cladding thickness of 0.375 inch 7000 6000 5000 j 4000 r 3000 2000 1000 O -
0.00 0.10 020 0.30 0.40 0.50 Eqtivalert Plastc Strain (in/in)
-. average straintrough cadding --- maximum strain thtough cladding A rnini mum strainthrough dadding Figure B 2 Equivalent plastic strain versus pressure for corrosion diameter of 4 inches and cladding thickness of 0.297 inch B-l
4.1.)JY 1 4000 3500 3000 t 2500 E 2000 mi = = ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a-1500 1000 r 4 4 4- 4 500 4 .4- 4- 4
. I . . . . . . . . . . . - I 0.00 0.10 0.20 0.30 0.40 0.50 Eqtivalert Plasc Strain Oin) average strain rough cadding -o ma)dmzn strainthrough cadding -niimurn strain through cadcing Figure B 3 Equivalent plastic strain versus pressure for corrosion diameter of 4 inches and cladding thickness of 0.240 inch I
D.
ol . . .. . I ! I I 0.00 0.10 0.20 0.30 0.40 0.50 Eqtivalert Plasc Strain(inln) average strainthtoughcdadding -_4mardmLrn strain through daddi,ng .-* mirimLrn straln trough daddirng Figure B 4 Equivalent plastic strain versus pressure for corrosion diameter of 4 inches and cladding thickness of 0.188 inch B-2
I 0
a-o0.00 li . 0.10 I 0.20 I. I 0.30
. I 0.40 0.50 Equivalent PlasUe Strain (inAn)
-e-average strainthrough dadding -si-maximum stain through dadding -- rmirimmn strain trough daddng Figure B 5 Equivalent plastic strain versus pressure for corrosion diameter of 4 inches and cladding thickness of 0.125 inch 0.00 0.10 020 0.30 0.40 0.50 Eqtivalent Plastc Stain (inlin)
-- average strain troughcEladding -maamumstraintroughcladding mirimurnmstraintroughcladding Figure B 6 Equivalent plastic strain versus pressure for corrosion diameter of 5 inches and cladding thickness of 0.375 inch B-3
I a
I oi I . .I 0.00 0.10 0.20 0.30 0.40 0.50 Equlvalert Plastic Srain (Intin)
-a- average strainthrough cladd¶ng --- mamntrn streintrugh daddng .-- minimrn strainthough daddng Figure B 7 Equivalent plastic strain versus pressure for corrosion diameter of 5 inches and cladding thickness of 0.297 inch 3000 2500 2000 a
e 1500 e.
oo O -
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Equivalert PlasEe Strain(iMn)
-- average strai n hrogh dadding -- maximum strain though dadding -*- mirimr strain through dadding Figure B 8 Equivalent plastic strain versus pressure for corrosion diameter of 5 inches and cladding thickness of 0.240 inch B-4
1600 I I I I I I 1 ! 1. !
1400 + 4
-t-1200 I'z ll G + +
! +
I
+- 4-8 1000 f1 +
E Sy800
( I - - ~~ 1
+
- 1 4- 4 600 1 *t- 1-t I 400 r r
1 4
I 1
1 200 4.
.4. 4 .4- 1 1 4-0 I- .. I 1 I -,----.-
, - 1..-.--
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Equivalert Plastc Stain (irAn)
-_ average staln tTough dadding - mmmurn stain trough daddng -- ririmum stainfrough claddlir Figure B 9 Equivalent plastic strain versus pressure for corrosion diameter of 5 inches and cladding thickness of 0.188 inch i
0.
0y 0.00 0.05 0.10 0.15 0.20 025 0.30 0.35 0.40 0.45 0.50 Eq.ivalent Plastz Stain (mirAn)
- average staintyough ciadding - maAmurn strain trough daddng -_-minimurn straintrough aciddng Figure B 10 Equivalent plastic strain versus pressure for corrosion diameter of 5 inches and cladding thickness of 0.125 inch B-5
I CL o l- , I . i . . . I i- iI i 0.00 0.05 0.10 0.15 020 025 0.30 0.35 0.40 0.45 0.50 Eqivalert Plas6c Strain (inin)
S--- verage strain ltrough daddir g -a- madmum strain ftough daddi ng -*- inrimum staintrough daddro Figure B 11 Equivalent plastic strain versus pressure for corrosion diameter of 6 inches and cladding thickness of 0.375 inch 3500 3000 2500 y, 2000 re 1500 1000 500 o ... .-.- 1-141 ,1 1-.- 1 -1 - 1 - 1 -1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Eqtivaent Plastc Strain (inin)
-*-mirimunstrain throughdadding -- average trainthroughdaddrog -- ma)dumstrain tloughedaddng Figure B 12 Equivalent plastic strain versus pressure for corrosion diameter of 6 inches and cladding thickness of 0.297 inch B-6
200 .-
1g4- I 1so K .I -
I il7 1~---- --
5ec ni. . -
0.00 0.05 0.10 0.15 020 025 0.30 0.35 0.40 0.45 0.50 Equ?aent Plutk Strain (h'h)
-& average strain fough dadding - mamum strain through claddng -*-minimum straintrough dadding Figure B 13 Equivalent plastic strain versus pressure for corrosion diameter of 6 inches and cladding thickness of 0.240 inch 1400 1200 1000 g 800 it 600 400 200 o,
0.00 0.05 0.10 0.15 020 0.25 0.30 0.35 0.40 0.45 0.50 EqLivalert Plasic Strain (inin)
-.- average stain trough claddirg -r madmum strain through dadding -_- mrimun strain through dacldding Figure B 14 Equivalent plastic strain versus pressure for corrosion diameter of 6 inches and cladding thickness of 0.188 inch B-7
7O 600 l 500 400 12 300 - - - - _
0.00 0.05 0.10 0.15 0.20 025 0.30 0.35 0.40 0.45 0.50 Eqivalert PlasbcStrain (irn)
-- average staIn trough daddirq - madmvm straintiTough caddng -*-mirimm stain ftough daddrq Figure B 15 Equivalent plastic strain versus pressure for corrosion diameter of 6 inches and cladding thickness of 0.125 inch B-8
250.00 200.00 2X 150.00 \
- t. ~Coolabil ity Limit xn 00.0 _Bumup < 30 GWdUMTU 4 ~He. = 230 cal/gm 1.0.00 . Fuel Rod Failure Threshold sl:
0.0- Bumup > 30 GWd/MTU Bmp<3 W/T 50 oo
_ Hc 251.7 - 0.3555*Bu - .01437*Bt? + 1.033x104-B3U3 Buu < 36 GWdca/gmT
- . 0.
Bumup > 36 GWd/MTU 0 _ ~~~~~Hr125 + 7058*exp(-.1409'Bu) 0 10 20 30 40 50 60 70 80 90 Rod Average Bumup (GWdlMTU)
Figure S-1 Revised Acceptance Criteria for the PWR REA and BWR RD events. The criteria are defined In terms of the radial average peak fuel enthalpy as a function of rod average burnup.
xi