ML031040222
| ML031040222 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse  |
| Issue date: | 07/03/2002 |
| From: | Matthew Kirk Office of Nuclear Regulatory Research |
| To: | Long S Office of Nuclear Reactor Regulation |
| References | |
| FOIA/PA-2003-0018 | |
| Download: ML031040222 (32) | |
Text
Mark Kirk - Fwd: Failure Model for 131
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From:
Mark Kirk1 To:
Steven Long Date:
7/3/02 4:13PM
Subject:
Fwd: Failure Model for DB Steve -
Attached please find a report from ORNL regarding the state of their model of DB in the 'as found' condition. Paul is currently putting the finishing touches on this report (please consider the attached only a draft).
The short summary of this report is as follows:
- 1. If we use a Weibull cumulative probability function to represent the uncertainty associated with the failure criteria we arrive at a predicted lower bound burst pressure of 6.65 ksi. Because the 3 parameter Weibull function has a finite lower bound value there Is - according to this model - zero probability of failure at pressures below 6.65 ksi
- 2. If Instead we adopt a Normal cumulative probability function to represent the uncertainty associated with the failure criteria we arrive at a cumulative probability of failure of 8.4E-1 0 at the operating pressure of 2.165 ksi. At a slight overpressure (2.5 ksi) the probability of failure goes up by about an order of magnitude to 8.9E-9. In either event, these are very small numbers.
Next week we will begin calculations on larger footprints for the wastage area Mark CC:
Paul - ORNL Bass, Richard - ORNL; Edwin Hackett; Nilesh Chokshi; Wallace Norris; Williams, 61 i' ormation
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Type of Document Authors:
Heavy-Section Steel Technology (HSST) Program Analysis of the Davis-Besse RPV Head Wastage Area and Cavity Letter Report P. T. Williams B. R. Bass Date of Document Responsible NRC Individual and NRC Office or Division September 2002 M. T. Kirk Division of Engineering Technology Office of Nuclear Regulatory Research Prepared for the U. S. Nuclear Regulatory Commission Washington, D.C. 20555-0001 Under Interagency Agreement DOE 1886-N653-3Y NRC JCNNoY6533 OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37831-8056 managed and operated by UT-Battelle, LLC for the U. S. DEPARTMENT OF ENERGY under Contract No. DE-ACO5-000R22725
ORNLNRCALTR-Analysis of the Davis-Besse RPV Head Wastage Area and Cavity P. T. Williams B. R. Bass Oak Ridge National Laboratory Oak Ridge, Tennessee Manuscript Completed - September 2002 Date Published -
Prepared for the U.S. Nuclear Regulatory Commission Office of Nuclear Regulatory Research Under Interagency Agreement DOE 1886-N653-3Y NRC JCN No. Y6533 OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37831-8063 managed and operated by UT-Battelle, LLC for the U. S. DEPARTMENT OF ENERGY under Contract No. DE-AC05-000R22725 2
CAUTION This document has not been given final patent clearance and Is for Internal use only. If this document Is to be given public release, it must be cleared through the site Technical Information Office, which will see that the proper patent and technical information reviews are completed In accordance with the policies of Oak Ridge National Laboratory and UT-Battelle, LLC.
This report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any agency thereof, nor any of their employees.
makes any warranty, express or Implied, or assumes any legal labilIty or responsibility for the accuracy, completeness, or usefulness of any Information, apparatus, product, or process disclosed, or represents that Its use would not Infringe privately owned rights. Reference herein to any specific commercial product process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or Imply Its endorsement.
recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.
3
Analysis of the Davis-Besse RPV Head Wastage Area and Cavity P. T. Williams and B. R. Bass Oak Ridge National Laboratory P. O. Box 2009 Oak Ridge, TN, 37831-8056 Abstract In support of ongoing investigations by the United States Nuclear Regulatory Commission's (NRC)
Office of Nuclear Regulatory Research, the Heavy-Section Steel Technology Program at Oak Ridge National Laboratory has carried out structural analyses of the damaged reactor pressure vessel (RPV) head located at the Davis-Besse Nuclear Power Station. This report presents the results of a finite-element analysis of the wastage area using submodeling techniques. A bounding case for the "as-found" condition of the cavity is developed and analyzed under static pressure loading conditions up to the point of failure.
The specific failure mode addressed by this analysis is incipient tensile plastic instability (i.e., plastic collapse) of the cladding. Wastage-area growth scenarios are also postulated based on assumed self-similar and ellipsoidal growth patterns, and the amount of exposed cladding surface area required to produce failure down to the nominal reactor coolant system (RCS) operating pressure is estimated for each growth pattern. Comparisons are made between the finite-element computational results and the burst pressure predictions from a theoretical model (center-membrane theory of Chakrabarty and Alexander (1970)) of failure in circular diaphragms under lateral pressure loading. A stochastic model, presented in an earlier report [1), is also applied to provide probabilistic estimates of the predictive uncertainty of the computational results.
For the bounded "as-found" case, the median predicted burst pressure, BPo., is 7.36 ksi for a cladding thickness of 0.24 in. and 5.73 ksi for a cladding thickness of 0.1825 in. For BP03 equal to the nominal operating pressure of 2.165 ksi, the center-membrane theory estimates a required diaphragm area of 498.9 in with a cladding thickness of 0.24 in. The value of 0.24 in. is the minimum cladding thickness obtained from UT measurements of the wastage area based on a 'A inch grid.
Estimates of failure pressure with associated probabilities can be calculated for a broad range of exposed cladding areas from the theoretical treatment of circular diaphragms due to Chakrabarty and Alexander (1970) in conjunction with the stochastic model described in a previous report [1]. The thin-walled membrane assumptions applied in the theory appear to better approximate the conditions in the exposed cladding as the wastage area increases in size. It is also observed that the shape of the footprint approaches a second-order effect as the footprint area increases.
4
1 Introduction 1.1 Objective In support of ongoing investigations by the United States Nuclear Regulatory Commission's (NRC)
Office of Nuclear Regulatory Research, the Heavy-Section Steel Technology Program at Oak Ridge National Laboratory has carried out structural analyses of the damaged reactor pressure vessel (RPV) head located at the Davis-Besse Nuclear Power Station. This report presents the results of a finite-element analysis of the wastage area using submodeling techniques. A stochastic model, presented in an earlier report [l], is also applied to provide probabilistic estimates of the predictive uncertainty of the computational results.
1.2 Background
Pursuant to the licensee's commitments to NRC Bulletin 2001-01 [2], the Davis-Besse Nuclear Power Station began a refueling outage [3] on February 16, 2002, that included inspection of the vessel head penetrations with an emphasis on the inspection of control rod drive mechanism (CRDM) nozzles. These inspections identified axial indications in three CRDM nozzles (Nozzles 1, 2, and 3, located near the center of the RPV head) that were experiencing pressure-boundary leakage. Upon completing boric acid removal on March 7, 2002, the licensee conducted a visual examination of the area and identified a large cavity in the RPV head on the downhill side of CRDM Nozzle 3. Followup characterization by ultrasonic testing (UT) indicated wastage of the low alloy steel RPV head material adjacent to the nozzle. The wastage area was found to extend approximately 5 inches downhill on the RPV head from the penetration for CRDM Nozzle 3, with a width of approximately 4 to 5 inches at its widest part.
See Fig. 1. for a photograph of the Davis-Besse RPV, a schematic of a typical nuclear power reactor showing the location of the CRDM nozzles relative to the RPV, and a sketch and photographs of the cavity and wastage area around Nozzle 3.
5
The above A s ows te Davis laseso actor vessel head degrdation between asoza a3 ad no*e #1t. This skltrh was prolded l mhe NRC by Me Lkensee.
Fig. 1. (a) Davis-Besse Nuclear Power Station RPV and (b) sketch of RPV head degradation.
6
Typical Pressurized Water Reactor Control Rod Cor Barrel Fig. 1 (continued) (c) schematic of a typical nuclear power reactor showing the relationship of the CRDM nozzles to the RPV head.
7
Reactor Vessel Head Degradation Location Fig. 1. (continued) (d) photographs of the wastage area and cavity with Nozzle 3 removed.
13 Scope Section 2 reviews the geometry and material properties used in the development of the finite-element global and submodels; Section 3 presents the algorithms used to estimate the growth patterns of the wastage-area footprint; Section 4 presents the results of both the bounding calculations for the "as found" condition of the wastage area and the growth-pattern results compared to the predictions of a theoretical treatment of failure in circular diaphragms; and Section 5 provides a summary and conclusions.
9
2 Geometry and Material Properties 2.1 "As-Found" Footprint Geometry Tables 1 and 2 present the details of the "as-found" geometry of the wastage area. The figure in Table 2 was taken from Fig. 13 of the Root Cause Analysis Report, Significant Degradation of Reactor Pressure Vessel Head, CR 2002-0891 [4]. The "as-found' footprint in Table 2 was digitized with CorelDraw 10i.
Additional details for the "as-found" case are given in [1].
2.2 Material Properties Three materials are used in the construction of the finite-element submodel of the wastage area:
(1) Alloy 600 for the CRDM tubes, (2) A533B for the base material of the vessel, and (3) SS308 for the subarc weld (SAW) cladding. Elastic properties [5] for these three materials are shown in Fig. 2 as a function of temperature. Figure 3 presents plastic properties [5] (effective stress as a function of effective plastic strain) for Alloy 600 and A533B pressure vessel steel. An adjusted SS308 stress vs. strain curve used in the bounding-case calculations is compared in Fig. 4 to curves from a range of A8W heats (SS304 pipe with SS308 weld from the PIFRAC database [5]) and the unadjusted stress vs. strain curve received from Framatome [6]. Strain hardening for the adjusted curve was reduced to lower-bound all of the data, where the offset yield strength and strain at ultimate strength were retained from the unadjusted SS308 curve. This adjusted stress/strain curve was applied in the "bounding" calculation for the "as-found" condition and all subsequent cavity growth cases.
23 Finite-Element Global and Submodels of Wastage Area and Cavity The submodeling capabilities of the ABAQUS finite-element code [7] were employed in this analysis to focus the available computational resources on the region of interest located around the wastage area cavity at CR.DM Nozzle 3. Submodeling can be used to investigate a portion of a model with a refined mesh. The boundary conditions of the submodel are driven by an interpolation of the displacement solution from an initial, relatively coarse, global model. The technique is primarily useful when it is necessary to obtain a refined, detailed solution in a local region, and the detailed modeling of that local region has a negligible effect on the global solution, i.e., solution information is passed in one direction only, from the global model to the submodel.
As shown in Figs. 5a and 6, the global model consists of the full RPV head (with all 69 penetrations) and closure flange. No cladding or CRDM nozzles are included in the global modeL The submodel (see Fig. Sb) consists of the cladding (SS308), base (A533B), and CRDM Nozzles (A600) 3, 11, 15, and 16.
The plan views of the RPV head in Fig. 7a and 7b indicate the position and geometry of the submodel 10
with respect to the global model. Figure 8 shows the ProEngineer solid model of the submodel. This solid model was imported into MSC Patran where the finite-element mesh was constructed.
Table 1. Wastage-Area-Footprint Geometry Data As-Found Footprint 1
35.36 30.36 16.4122
.0.1194 98.89 9699.33
-117.16 75.26 197.41
'0.9004.4.4351>
'0.4351.0.9004>
Adjusted Footprint 0.25 in 40.06 31.72 16.4301
-0.1255 129.02 11031.82
-141.35 99.00 245.71
<0.1943,-.4476> <04476,0.8943' for Bounding Calculaztio Fortprint cenrroid is in global coordinates.
Global coordintne syste bas dt a-axis aligned with the vertical eentedre of the vessel.
The xz-y pane ofthe global coordinate systemn is a horizontal plane with the x-axis along the line between the centerlines of Nozzles 3 and I1.
"Adjusted" Footprlnt a - 0.25 In.
Area - 40.06 in' Perimeter - 31.78 In.
I FY q
= r, + a.
= -r, cos(+,)
"As Found" Footprint
= r, sin(4)
Area - 35.36 In' Perimeter - 30.36 In.
2.4 Loading and Constraint Conditions Only mechanical loading due to the intemal pressure of the coolant was considered in these analyses. The.
pressure load was applied to the inner surface of the vessel and the inside of the CRDM nozzles. Tied contact constraints were established between the cladding and base material interface and between the CRDM nozzles and the cladding and base. The J-groove weld attaching the nozzle to the vessel was not explicitly modeled. The vertical surfaces of the submodel were driven by the interpolated displacement solution obtained with the global model of the RPV head (see Fig. 5).
11
Table 2. Details of Wastage Area Footprint Before Adjustment for Bounding Calculation (Figure taken from Fig. 13 ref. 141)
ArL of OvcrflTw Dikxin Putts orrFcle NI 0
-0.639
-1.895 24 8.000 0.334 1
-0.334
-2.280 25 7.500 0.483 2
0.000
-2.235 26 7.000 0.582 3
0.500
-2.492 27 6.500 0.829 4
1.000
-2.522 28 6.000 1.046 5
1.500
-2.482 29 5.500 1.303 6
2.000
-2.581 30 5.000 1.778 7
2.500
-2.730 31 4.500 2.460 8
3.000
-2.769 32 4.000 3.023 9
3.500
-2.759 33 3.500 3.300 10 4.000
-2.789 34 3.000 3.221 11 4.500
-2.819 35 2.500 3.250 12 5.000
-2.819 36 2.000 3.300 13 5.500
-2.759 37 1.500 3.349 14 6.000
-2.700 38 1.000 3.240 15 6.500
-2.621 39 0.500 3.122 16 7.000
-2.512 40 0.000 3.000 17 7.500
-2.364 41
-0.210 2.578 18 8.000
-2.216 42
-0.364 2.000 19 8.500
-2.087 43
-0.242 1.985 20 9.000
-1.712 21 9.135
-1.000 22 9.000
-0.555 23 8.500 0.137 Origin of local coordinate system located at centerline of Nozzle 3. (inches) 12
32000 c
a:
is a
.2 V
U aaI (a) 0 200 400 600 B00 Temperature ('F) 08 1000 0612002.Kl ptw a] A -...
0.38 S
0:
aA1 aIL 0.36 0.34 0.32 0.3 A5338 I
.I I
I I
I I
0.28 0.26 -
0.24 0
200 400 600 Temperature (F) 800 1000 (b)
W
/2002.K2 ptw Fig. 2. Elastic properties 15J of the materials used In the rwite-element models of the wastage area:
(a) Young's elastic modulus and (b) Poisson's ratio.
13
140 a1 i
(a I
120 100 80 60 40 20 0
0.05 0.1 0.15 0.2 0.25 Effective Plastic Strain (a) a 0
CO (b)
- 900 6000
.1700 !
600 500 0
400 w
300 I 200 0.3 0.35 03I14"2.K3 ptw 800 600
'801 OF I
4001 200 0
0.15 03l1420ZK2 phw 140 120 100 80 0
0 0.05 0.1 Effective Plastic Strain Fig. 3. Plastic property data 151 used in global and submodel: (a) Alloy 600 and (b) A533B pressure vessel steeL 14
J 80 Framatomne
=
=114.992 s 5
SS308 Curve OUU F-'
to Je 0
0 2
I
= 69.65 ksi a,,,= 61.64 Wsi 60k Adjusted SS308 Curve for Bounding Calculation
)8 curves 1 Ce = 94.359 80.194 1 1true 40 For both SS3(
Ofli7.3%,,,
30.96 Wi uniform elongation - 11.15%1I 20 K At 600 OF E 25,571 Wsl v- 0.295
-~
-b-A8W-101 A8W-102 A8W-103 A8W-104 A8W-105 A8W-106 A8W data at 550 aF ChI I
I i
I I
I I
I I 1 0
0.05 0.1 True Strain (-)
0.15 0.2 06/1012002.Ki ptw Fig. 4. Adjusted SS308 stress vs. strain curve used In the bounding-case calculations compared to curves from a range of A8W heats 15]. Strain hardening In the adjusted curve was reduced to lower-bound all of the data. The offset yield strength and strain at ultimate strength were retained from the unadjusted SS308 curve received from Framatome 16].
15
(a)
Submodel of Wastage Area 16,935 elements 52,887 nodes Nozzles 3, 11, 15, and 16 Base Material with Wastage Area ptw VI 1202 (b)
V Fig. S. Finite-element global and submodels of the Davis-Besse head and wastage area. The displacements at the vertical side boundaries of the submodel are driven by the global model. Both models are exposed to the same Internal pressure loading.
16
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o a
/
l~ ~
0 O a 6 a O
o o F
ooo tooI 0 o 0 o T o G 0 O
-T r _
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- a rE
_ e I -
T -
N -
p 1, Wk
_7
- -T-MCJCALMAC. MM.
ew4ORAMU r
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Oak Ridge Natinfal Labgi'mcry Davis-Besse RPV Head and aosure Flange A
I n
m c
H 4
I m. o.j I
.1.
r_+_
C WD!_
Fig. 6. Geometry of RPV head and closure flange used In global model.
17
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0 0
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AJIL Fig 7. (a) Relative location of submodel within full RPV head, Is
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ATE I OATE S)BtT Fig. 7. (continued) (b) geometry of submodel relative to Nozzles 3, 11, 15, and 16.
(b) 19
.fl-,.-
A4m..dm.4pi
4-&2a m.
,Am*4U1.h-N P.m.iwqJL7gIa.
Ccnmadol
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1IJA.4III Fig. S. Geometry of adjusted wastage area footprint. Lower figure Is a Photoworks-rendered Image of the submodel with the adjusted 'as-found" footprint.
20
3 Postulated Growth Patterns 3.1 Self-Similar Growth Pattern The self-similar growth-pattern scheme attempts to maintain, as closely as practicable, the general shape of the "as-found" cavity footprint. New growth footprints are scaled from a local coordinate system with its origin positioned at the centroid of the "as-found" footprint. A position vector, r., tracks the profile of the footprint using the polar coordinates (,,O) at the 44 points defined in Table 2. At each point along the footprint, the magnitude of the position vector is increased by a constant scaling factor, a, and then mapped back to the local rectangular Cartesian coordinate system by the following algorithm for i = 0,43 to, =
r, = ax r, l
x, = -or, cos(o,)
y1 = rsin(O,)
as shown in Fig. 9. This local coordinate system is subsequently mapped to the coordinate system used in the ABAQUS global model and submodels. Figure 10 shows the five growth patterns investigated for a ={1.6,2.0,2.8,3.0,3.4}. The scaled footprint's centroid, perimeter, area, and higher moments were calculated with AutoCad 2002 by converting a closed spline to a region and then applying AutoCad's Region Mass Properties utility. These footprint details are given in Table 3. The exposed-cladding surface area ranged from 86 to 276 in2. Four of the five growth patterns (as indicated in Fig. 10) intercepted and were constrained by the outer boundaries of the submodel. A second growth-pattern scheme was developed to check the sensitivity of the results to this interaction with the submodel boundaries.
3.2 Ellipsoidal Growth Pattern In Fig. I1, the ellipsoidal growth-pattem scheme established a partially elliptical or ovalized footprint extending between Nozzles 3 and 11. The growth is parameterized by the variable 5 which serves as the transverse (initially minor) axis footprint extending between the two nozzles. The longitudinal (initially major) axis also varies. The exposed-cladding surface area ranges from 99 to 254 in2 for the ellipsoidal growth patterns.
21
As-Found Footprint Area = 35.36 in2 Perimeter = 30.36 in.
,Centroid of (16A4122,-0.1194)
/11
15K t e
i~~r
- 441)
Hoof He I~
rib2-a rk Self-Similar Scaling x;= -r, cos(WI a = SS scale factor
,= r, sin(4,)
Fig. 9. Local coordinate system employed In self-sinilar growth patterns with scaling of footprint based on scale factor, a.
Self-Similar Growth Patterns f D
D Fig. 10. Expansion of self-similar growth patterns constrained at submodel boundaries.
22
Ellipsoidal Growth Patterns
- 2)
(6) 15 6,61n.; A= 40.85 in>.
6 5 10 in.; A a 99.3 In' 6=20 in.; A=218.1 in' 8 =20 in.; A =253.6 in' Fig. 11. All ellipsoidal growth patterns contained within submodel boundaries.
23
4 Results and Discussion Table 3 presents the results of cavity-growth calculations using the ABAQUS finite-element submodels of postulated wastage areas for the two growth pattern schemes described in Sect. 3. The pressures calculated at numerical instability are compared in Fig. 12a to burst pressures for circular diaphragms estimated by the critical-strain theory of Chakrabarty and Alexander [8]. The finite-element analyses applied a nonlinear finite-strain procedure with an incremental pressure load increasing from zero up to the load at which numerical instabilities caused ABAQUS to abort the execution. The internal pressure attained immediately preceding the onset of numerical instability was designated in [1] as the pressure at numerical instability, PM. This calculated pressure is linked to an estimated failure pressure with an associated probability through the application of a stochastic model developed in [1].
The theoretical treatment of critical strains in circular diaphragms under lateral pressure loading is discussed in refs. [1, 8, and 9]. In summary, the application of the theory to the wastage-area problem proceeds as follows:
Calculate the effective critical strain [8].
- 1. =2(2 - nXI + 2n) 11-4n Calculate the corresponding effective critical stress.
Calculate the critical thickness.
- Calculate the polar height at the critical-strain.
- Calculate the corresponding bulge curvature radius.
- Finally, calculate the predicted diaphragm burst pressure.
hot = h exp(-e )
H., =a e LcxpiE I-1 H,,, + a 2H.
pan = 2hr,,*,f R2h2 From the SS308 properties of the bounding case with a clad thickness of 0.24 in. and the geometry of Fig. 13, the following variables are set n = 0.1941 K = 94.359 ksi he = 0.24 in.
a = (Area/ir)"2 in.
24
Iu.u T Clad Thickaess a 024 Inches SS 308 bounding stres-straln curve 0.0 L
E 7.0 L
40 M
E50
.23 la
- 0.
3.0
'As-Found'
- Sel-Similar Growth i kg As Fourd I
- Ellipsoidal Grow I - - Operasng Pressure
- -- Set Point Chrabarly and Alexander (1970)
Circular Diaphragms (CentmrMembrane Fallure Theory)
- 5. Poht Pmsu A"Mtwur<........-
1.0 6.0
'1.
krabarty and 1 M. Aicucndce 1{ydrmlsatic Bulging of Circular Di~phgmss.Jh-n-of2f1atnbI. St]). 11970) 155-141.
I s0 100 ISO 200 Footprint Area (In')
250 300 S50 (a) 10.0 U
n 2
IL I"U la 2
0.
0 50 100 150 200 250 300 350 (b)
Diaphragm Area (in2) phv20-20W Fig. 12. Failure pressures as a function of footprint area: (a) pressures at numerical Instabity, PNI, calculated by ABAQUS finite-element submodels of postulated footprints are compared to burst pressures in circular diaphragms predicted by the theory of Chakrabarty and Alexander (1970) and (b) stochastic failure model scaled from the theory of Chakrabarty and Alexander (1970).
25
In general, the finite-element Pw predictions in Fig. 12a can be observed to follow the trends predicted by the theory of Chakrabarty and Alexander [8] when the exposed-cladding footprint area serves as the primary independent variable. As the exposed-cladding area increases, the agreement between computational and theoretical predictions improves. This improvement may be in part due to the increasing validity of the "thin-walled membrane" assumptions applied in the theoretical model.
The theoretical model assumes that the critical strain occurs at the maximum polar height of the spherically-deforming membrane. Edge effects in the diaphragm are not considered, and the theory focuses on failure at the center of circular diaphragm only. From inspection of the plastic strain contour plots near failure in the finite-element models, it was observed that the maximum plastic strains occurred along the edges of the footprint, thus indicating a higher probability of edge failures rather than center failures. One explanation for the good agreement between the center-membrane failure theory and the computational results may be that, even though failures may be more likely to occur first at the edges of the footprint, as the area increases failure within the interior of the footprint (as predicted by the theory) may also be imminent.
Table 3. Case Matrix and Failure Pressure Results T
At-Found Fotrt I
35.36 30.36 16.4122
.0.1194 98.9 9699.3
-117.2 AdjustedFootprint additive l
6.01 7.35 8.99 0.24 40.06 31.78 16.4301 0.1255 129.0 11031.3
-4143 forBounding
+02i.
4.U 5.73 7.00 0.2325 40.06 31.78 16.4301 0.1255 129.0 11031.1
-141.3 Calulation Self-Similar 1.6 482 436 5.33 6.52 0.24 16.04 50.09 16.1199
.0.0503 659.4 23404.4
-395.0 Self-similar 2.0 3.33 3.01 3.63 4.50 0.24 130.95 65.19 15.8900
- 0.0450 1593.8 35503.8
-832.4 selr-similar 2.3 2.75 2.49 3.04 3.72 0.24 191.37 79.54 18.0930 405830 4017.2 72416.6
.4117.S Self-similar 3.0
- X60 235 2.37 3.51 0.24 235.30 76.60 13550
-0.7060 49795 93743.1
.5599.1 Sd-similar 3.4 233 2.11 2.53 3.15 0.24 276.28 30.36 19.2100
-1.0140 6840.7 116363.9 4425.6 Ellip!oidal 10
- 3.
3.40 4.16
- 5.
00.24 99.32 43.23 11.9810.0.0090 766.3 417162
-12.0 Ellipsoidail 20
.1 2.65 324 0.24 213.06 59.02 18.7660 *0.0170 615S.1 34305J *45.1 Ellipsoidal 20a 4
1.94 237 2.39 0.24 253.65 63.26 19.3330 *0.0190 7302.3 104200.3
-59.7 Ellipsoidal 20a0 2.2 1.97 2.41 2.93 0.24 253.65 63.26 19.3330 *0.0190 7302.3 104200.3
-59.7 Ellipsoidal 6.2 LFi 5.42 6.62 3.10 0.24 40.35 23.1 15.9500 0
123.1 140133
-0.3
- Sane as previsus cs. exeept Nozle 1I eoIns d from vertical displacement Footrint entroid is in global coordinates.
Global coordinate system has its z-ais aligned with die vertical centerine of die vesseL TMe xvy plane oftie global coordinate system is a horizontal plane witd die x-axis along the line between te centedines of Nozzl 3 and 11.
26
I I
Fig. 13. Spherical geometry of deformation assumed in plastic instability theory [8].
The quantile curves shown in Fig. 12b are determined from the LogLaplace stochastic model developed in [1] and scaled by the burst pressure predictions from the Chakrabarty and Alexander model [8] using a diaphragm thickness of 0.24 in. and the bounding stress-strain curve shown in Fig. 4. With the service pressure, SP, as the random variate, the three-parameter Log-Laplace continuous distribution has the following probability density functionfmL, and cumulative distribution function, FLt, fO(SPja,b,c)=' jc( SPa for a >0, c (Sa 2
,a< F1 12bI b ) ;SP~b 2
a
(<SP<
,,p(S~j~b~c=
l(SP-a %1c I--
- SP~
- b (bc) > 0 (2) fora2O, (bc)>O and the percentile function (inverse cumulative distribution function) is QLp(P bc)
BPP =l a+exp[ln(b)+ n(2P)J
- pS0.5 (3) for (O<p<1)
- p >0.5 C
27
where BP, is the predicted burst (failure) pressure with probability p, a is the location parameter, b is the scale parameter, and c is the shape parameter. The fitted parameters from [1] were:
a=0 b = 1.1057xP..dd (4) c = 11.45441 where P,,O*, can either be the pressure at numerical instability, PmI, calculated from a finite-element model based on a given cavity configuration and cladding thickness or the burst pressure calculated from the center membrane theoretical model of Chakrabarty and Alexander [8] (see Fig. 12b). The median predicted failure pressures given in Table 3 are calculated from the Pm values by observing from Eq. (3) that median predicted failure pressure = BPO5 = b x Pv, = 1.1057 x P.7 (5)
For the bounded "as-found" case, the median failure pressure is 7.35 ksi for a cladding thickness of 0.24 in. and 5.73 ksi for a cladding thickness of 0.1825 in.
The diaphragm areas in Table 4 correspond to two service pressures, an operating pressure of 2.165 ksi and a safety-valve set-point pressure of 2.5 ksi. The cumulative failure probabilities are scaled from the predictions of the Chakrabarty and Alexander [8] theoretical model with a diaphragm thickness of 0.24 in.
and the bounding SS 308 stress-strain curve from Fig. 4.
Table 4. Diaphragm Areas at Two Pressures Over a Range of Failure Probabilities 1%
164.4 123.3 5%
217.7 163.3 50%
325.4 244.0 95%
486.4 364.8 99%
644.3 483.2
( Operating pressure 2.165 ksi (2) Safety-valve set-point pressure = 2.5 ksi Diaphragm thickness - 0.24 in.
SS 308 Cladding properties 28
5 Summary and Conclusions This report has presented the results of finite-element analyses (using the submodeling techniques available in the ABAQUS computer code) of the Davis-Besse RPV head in the region of the wastage area around Nozzle 3. These finite-element analyses applied a nonlinear finite-strain procedure with an incrementally increasing pressure load applied from zero up to the load at which numerical instabilities caused ABAQUS to abort the execution. The internal pressure attained immediately preceding the onset of numerical instability is designated as the pressure at numerical instability, Pma [1]. For a bounding calculation of the "as-found" condition, the Pm, was calculated to be 6.65 ksi. Depending on the shape of the wastage footprint, the required exposed-cladding area for the PNI to occur at an operating pressure of 2.165 ksi ranged from approximately 254 in.2 to 280 in.'. The application of a vertical constraint to the top of Nozzle 11 (see the Ellipsoidal Case 20a* in Table 3) produced a small increase in the value of PI.
The center-membrane theory of burst pressure for circular diaphragms produced trends (as a function of effective diaphragm area under load) that followed the observed trends for the irregular geometries of the growth-pattern wastage areas investigated in the current study. Associated cumulative probabilities are provided based on a stochastic model described in a previous report (1]. For the bounded "as-found" case, the median predicted failure pressure, BPgj, is 7.35 ksi for a cladding thickness of 0.24 in. and 5.73 ksi for a cladding thickness of 0.1825 in. For BPO.5 equal to 2.165 ksi, the center-membrane theory estimates a required diaphragm area of 325.4 in2 with a cladding thickness of 0.24 in. The value of 024 in. is the minimum cladding thickness obtained from UT measurements of the wastage area based on a hi inch grid as depicted in Fig. 14 of ref. [4].
Estimates of failure pressure with associated probabilities can be calculated for a broad range of exposed cladding areas from the theoretical treatment of circular diaphragms due to Chakrabarty and Alexander
[8] in conjunction with the stochastic model described in a previous report [1]. The thin-walled membrane assumptions applied in the theory appear to better approximate the conditions in the exposed cladding as the wastage area increases in size. As can be observed in Fig. 12, the shape of the footprint approaches a second-order effect as the footprint area increases.
At the time of this writing, data from a "dental" molding of the wastage-area cavity became available.
Figure 14 compares the footprint derived from a photograph of this molding with the footprint used in these analyses obtained from [4]. It can be observed from Fig. 14 that the wastage area assumed in this report is conservatively larger than the footprint estimated from the recent molding.
29
Magnification: 6"13.82" -. 37X
_S._
-,.E
-ev Ad
-a em as it*
(a)
Area Of PrOtO: (6")(1-57 X M(4-St.
IA O
A,=% of OverOnu DuriV Puts of Cyclo i
Footpint used In current atud 4~~t-r is TV
->4Y 41---
(b)
FoplrIt from cavity mold Fig. 14. Comparison of recent characterization of wastage-area footprint with geometry used In the current study: (a) photograph of cavity mold and (b) footprint used In current study and footprint estimated from cavity mold.
30
References
- 1. P. T. Williams and B. R. Bass, Stochastic Failure Model for the Davis-Besse RPV Head, ORNL/NRC/LTR-???, under review.
- 2. NRC Bulletin 2001-01, "Circumferential Cracking of Reactor Pressure Vessel Head Penetration Nozzles", August 3, 2001.
- 3. -Recent Experience with Degradation of Reactor Pressure Vessel Head, NRC Information Notice 2002-11, United States Nuclear Regulatory Commission, Office of Nuclear Reactor Regulation, Washington, DC, March 12, 2002.
- 4. S. A. Loeblein, Root Cause Analysis Report, Significant Degradation of Reactor Pressure Vessel Head CR 2002-0891, Davis-Besse Power Station, April 15, 2002.
- 5. Personal communication with Computational Mechanics Corporation of Columbus, Columbus, OH, March 2002, Data from PIFRAC database.
- 7. ABAQUS/Standard User's Guide, Volume !, v6.2-4, Hibbitt, Karlsson, and Sorensen, Inc., Pawtucket, RI, 2001.
- 8. J. Chakrabarty and J. M. Alexander, "Hydrostatic Bulging of Circular Diaphragms," J. Strain Anal.
5(3), (1970) 155-161.
- 9. RP Hill, "A Theory of the Plastic Bulging of a Metal Diaphragm by Lateral Pressure," Philos. Mag.
(Ser. 7) 41, (1950) 1133.
31