ML030850185
| ML030850185 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse |
| Issue date: | 02/05/2003 |
| From: | - No Known Affiliation |
| To: | Office of Nuclear Reactor Regulation |
| References | |
| FOIA/PA-2003-0018 | |
| Download: ML030850185 (34) | |
Text
PRELIMINARY Response to Question A The size of the degradation cavity and the transition from the cladding thickness to the head thickness used in the calculation reflected what was the best available at the time of the calculation. More work is currently in progress on the removed damaged cavity to determine the exact size and geometry of the cavity and the transition regions.
Question B Is there sufficient mesh refinement through the cladding thickness to adequately capture the bending and shear strains at the edge of the cavity? Describe any sensitivity studies used to demonstrate the adequacy of the mesh refinement.
Response to Question B In the analysis of the wastage cavity, six elements were used through the thickness of the cladding. A convergence study, using both an axisymmetric model and a three dimensional model was performed in Reference 2 to evaluate the impact of the number of through-wall elements in the thickness of the test specimens. The results indicate that there is no significant difference in the burst pressure predictions when the number of through-wall elements is increased from six to 12. Therefore, it is concluded that the analyses of the wastage categories with six elements through the thickness represents a converged solution.
Furthermore, when fewer elements than six were used in the convergence study, it resulted in conservative estimates of the burst pressures.
Question C Was the cladding deposited by weld wire? Do the thinner cladding thickness measurements from UT coincide with the locations of weld bead toes? In what direction do the cladding weld beads run relative to the long axis of the degradation cavity?
Response to Question C The cladding was deposited by weld wire. It is difficult to determine if the thinner cladding thickness measurements from the UT coincided with the location of the weld bead toes since the UT measurements were taken on one-inch grids and as such, there was not adequate resolution to make such a determination.
It is also difficult to determine the direction of the cladding weld beads from the available information.
Additional investigation of the removed damaged cavity is currently in progress that might provide more information.
NGC-02-039
PRELIMINARY References
- 1) P. C. Riccardella, "Elastic-Plastic Analysis of Constrained Disk Burst Tests," ASME Paper No.
72-PVP-12, Proceedings of Pressure Vessel and Piping Conference, New Orleans, LA, September 17-21, 1972.
- 2) Structural Integrity Calculation W-DB-OlQ-304, Rev. 0, "Evaluation of Failure Criterion Used in Elastic-Plastic Analysis of Davis-Besse RPV Head Wastage."
NGC-02-038
PRELIMINARY Table 1: Tensile Test Data for 304 Stainless Steel at 550°F Reference YS ksi UTS ksi Elong %
RA %
Matl Type NUREG!CR-6235 20.8 62 38.4 70 8 Base NUREG!CR-4538 22.2 67.3 39 70.8 Base NUREG/CR-4538 22.8 68.8 40.5 70.8 Base NUREGICR-4687 20.1 65.2 53.8 71.3 Base EPR. NP-4768 23.1 61.3 47 74 Base EPRI NP-4768 24.8 62.6 45 70 Base EPRI NP-4768 33.2 72.7 42 67 Base ASME 72PVP 12 34 84 54 75 Base Ave.Base 45.0 71.2 EPRI NP-4668 44.8 62.9 22 46 SAW EPRI NP-4768 36 61.8 25 67 SAW EPRI NP-4768 40.8 70.3 25 69 SAW NUREG/CR-6098 37.4 68 26.4 SAW NUREG/CR-6389 49.1 68.1 30 46 SAW NUREG/CR-6389 45 67.1 33 42.4 SAW NUREG/CR-6389 54.3 74 15.5 63 SAW NUREG/CR-6389 51.8 71.8 13.7 54 SAW NUREG/CR-4878 471 67.6 31.5 44.2 SAW NUREG/CR-4878 28.3 67.5 34.5 47 SAW-Ann Ave.SAW 25.7 53.2 EPRI NP-4668 45.7 65.1 26 58 SMAW EPRI NP-4768 46 8 61.4 37 48 SMAW EPRI NP-4768 49.4 64.7 35 46 SMAW NUREG/CR-4878 40.8 70.3 24.8 68.6 SMAW Ave.SMAW 30.7 55.2 NUREG/CR-4538 44.3 65.4 33 74.3 Weld NUREG/CR-4538 42.2 64.3 30 72.9 Weld lAve.SAW&SMAW 27.3 53.8 NGC-02-038
PRELIMINARY SSTRUCTURAL CALCULATION FILE No: W-DB-OIQ-304 INTEGRITY Associates, Inc.
PACKAGE PROJECT No: W-DB-O1Q PROJECT NAME: Operability and Root Cause Evaluation of the Damage of the Reactor Pressure Vessel Head at Davis-Besse CLIENT: First Energy Corporation CALCULATION TITLE: Evaluation of Failure Criterion Used in Elastic-Plastic Analysis of Davis Besse RPV Head Wastage PROBLEM STATEMENT OR OBJECTIVE OF THE CALCULATION:
Develop a finite element model to simulate actual test data to evaluate the effectiveness of the failure criteria used in the elastic-plastic stress analysis of Davis-Besse RPV head wastage cavity.
Project Mgr.
Preparer(s) &
Document Affected Revision Description Approval Checker(s)
Revision Pages Signature &
Signatures &
Date Date 0
1 -28 Original Issue Al - A2 BI -B9 Project CD-Rom PAGE 1
of 28
PRELIMINARY 1.0 Introduction During recent in-service inspections of the reactor pressure vessel (RPV) head and penetrations at Davis-Besse, significant wastage was observed in the vicinity of control rod drive mechanism (CRDM) No. 3. A calculation package was prepared for First Energy [1] to determine the limiting pressure load of the damaged RPV head.
Based on the review of this calculation package, the NRC raised a number of questions (See Appendix A), the majority of which were concerned with the failure criteria used in the evaluations.
The purpose of this calculation is to develop a better understanding of the failure criteria as used and its relative "conservativeness" in regards to the failure pressure.
2.0 Technical Approach The failure criterion used in Reference I was set such that the maximum strain could not exceed the ultimate tensile strain. Hence for the stainless steel cladding where the maximum strain is expected to occur, the maximum equivalent total strain is limited to the maximum strain of 11.15%
(corresponding to the ultimate strain for the stainless steel cladding in Reference 2) through the thickness of the component.
In order to evaluate the reasonableness of this failure criterion, the results of the failure pressures predicted with this criterion were compared against test results of very similar geometries. Disk burst test, similar to the Davis-Besse head wastage geometry were performed under the auspices of the PVRC Subcommittee and documented in and ASME publication [3] (see Appendix B for the actual publication).
Described in Reference 3 were a series of burst tests using machined disks of various materials. The test disk dimensions and the illustration of the test setup are shown in Figure 1. The materials tested included 304 Stainless Steel, A-533 Grade B Low Alloy Steel and A85 Grade C Carbon Steel. For the purposes of this calculation, only the 304 Stainless Steel testing will be reviewed.
As can be seen in Figure 1, three basic disk geometries were tested. In order to evaluate the effectiveness of the failure criteria developed for Reference 1, the same failure criteria will be used to determine the disk burst pressures. As a result, a series of finite element models were developed using the test disk dimension provided in Reference 3. The models were created and evaluated using the ANSYS finite element software [4]. The actual evaluations and subsequent failure criteria comparison are included in the following sections.
PRELIMINARY 3.0 Finite Element Models A series of finite element models were constructed to determine burst pressure for the various disk configurations. Initial studies were performed using an axisymmetric model but subsequent evaluations included three-dimensional modeling similar to that used in Reference 1.
The elastic material properties for all evaluations were for 304 stainless at room temperature as defined by Reference 5. These values used were as follows:
Modulus of Elasticity, E, e6 psi: I28.3 Poisson's Ration, v:
0.3 The plastic material properties for stainless per Reference 3 were:
[1] Stress Strain Curve Assumed to be of form c =A (E)"
Therefore the stress-strain curve used in all of the evaluation is shown in Table 1. Any additional model specific conditions will be described in the following sections.
PRELIMINARY
PRELIMINARY Table 1 Stress Strain Curve for 304 Stainless Steel 131 Strain (in.in)
Stress (psi) 0 000 0
0.025 31208.63 0050 43952.49 0075 53699.79 0100 6190024 0.125 6911397 0.150 75627.79 0.175 81611 83 0.200 8717684 0225 9239968 0.250 97336.26 0275 102028.8 0300 106510 0.325 110805.8 0.350 114937.5 0.375 118922.4 0400 122775 0.425 126507.5 0.450 1301306 0475 133653.1 0.500 137083 0525 140427.1 0550 143691.6 0.575 146881.9 0.600 150002.7 0.625 153058.4 0650 156052.8 0.675 158989.5 0700 161871.6 0725 164702.2 0 750 167483.7 0.775 170218.7 0 800 172909.5 0.825 175558 0850 178166.2 0.875 180735 8 0.900 1832686 0.925 185766 01950 188229.5 0.975 2090660.
1.000 193060 1.025 195429.4 1.050 197769.7 1.075 20DO82 i.100 202367.3 1.125 204626 4 1.150 206860.2 1.175 209069.7 1.200 2112554 1 225 213418.2
PRELIMINARY 3.1 Axisymmetric Finite Element Model The axisymmetric models were developed in ANSYS using the 2-D 8-Node Structural Solid element, PLANE82. All three geometries described in Reference 3 were evaluated as was the effects of the finite element mesh density on the onset of numeric instability. A total of 5 evaluations for each disk geometry were made, the only difference between each evaluation was the mesh density, which can be simplified to the number of elements through the thickness of the thinned portion of the disk. As such, the mesh densities that were evaluated where 4, 6, 8, 10 and 12 elements through the thickness. Figure 2 shows the progression of mesh density for geometry-A.
The mechanical boundary conditions for these evaluations consisted of simple vertical restraint throughout the approximate clamp region. This region was assumed to into the entire region of the disk, which remained at the full 1 inch thickness. See Figure 3 for an example of the applied boundary conditions on the 4 element through thickness, geometry-A model.
3.2 Three-Dimensional Finite Element Model The three-dimensional models were developed in ANSYS using the 3-D 8-Node Structural Solid element, SOLID45. All three geometries described in Reference 3 were evaluated as was the effects of the finite element mesh density on the onset of numeric instability.
Only a 30' section of the total disk was modeled since the loading and geometries were also symmetrical. Two evaluations for each disk geometry were made; the only difference between each evaluation was the mesh density, which again can be simplified to the number of elements through the thickness of the thinned portion of the disk. As such, the mesh densities for the 3 dimensional models that were evaluated were 4 and 6 elements through the thickness. It should be noted that the stainless clad for the actual Davis-Besse cavity evaluation used 6 elements through the thickness. Figure 4 shows the two mesh densities for geometry-A.
The mechanical boundary conditions for these evaluations used the same vertical restraints as the axisymmetric evaluations. In addition, axisymmetric boundary conditions were applied to the free ends of the disk, the preventing translations in the circumferential direction. This results in the centerline of nodes being limited to translation in only the vertical direction See Figure 5 for an example of the applied boundary conditions on the 4 element through thickness, geometry-A model.
4.0 Loading All of the evaluations were loaded in the same manner. An incremental pressure was applied to the cavity surfaces until numeric instability was reached. See Figure 6 for an example of the applied pressure.
PRELIMINARY
PRELIMINARY 5.0 Mesh Density Results For each evaluation, the pressure was allowed to rise incrementally until numeric instability occurred. The points of instability, as compared to the actual disk burst tests, are shown in Table 2.
Table 2 Mesh Density Effects of Numeric Instability Model Pressure (psi)
Predicted/
Model Type Through-Wall Numeric Actual Test Test Result
__oe___ype___
Elements Instability Burst
(%)
Axisymmetric 4
12725 84.8 Axisymmetric 6
13942 92.9 Axisymmetric 8
14004 93.4 Axisymmetric 10 14022 15000 93.5 Axisymmetric 12 14005 93.4 3-Dimensional 4
13979 93.2 3-Dimensional 6
13997 L
93.3 Axisymmetric 4
5929 87.2 Axisymmetric 6
6630 97.5 Axisymmetric 8
6695 98.5 Axisymmetric 10 6695 6800 98.5 Axisymmetric 12 6694 98.4 3-Dimensional 4
6671_6688_
98.4 3-Dimensional 6
6671 98.1 Axisymmetric 4
6317 82.0 Axisymmetric 6
6962 90.4 Axisymmetric 8
6997 90.9 Axisynmetric 10 6998 7700 90.9 Axisymmetric 12 6997 90.9 3-Dimensional 4
6976 90.6 3-Dimensional 6
6974 90.6 The results are also shown graphically in Figure 7.
PRELIMINARY 6.0 Total Strain Results Based on Section 5, only the highest through-wall element count cases will be further evaluated. As a result, Figures 8 though 10 show the total Von Mises Strain just prior to onset of instability for the 12 through-wall element axisymmetric model and Figures 11 through 13 show total Von Mises Strain for the 6 through-wall element 3-D model.
7.0 Strain Criteria Comparison The original failure strain criterion described in Section 2.0 indicated that when the through-wall total strain exceeded the uniform elongation percentage, the structure would be considered to have failed. As a check of this criterion, the total Von Mises nodal strains as they varied with pressure were extracted from the middle of the modeled disk at the top, middle and bottom of the wall thickness. The resulting strains were then plotted versus the pressure and compared to the actual burst pressure measured in Reference 3 and the failure pressure as defined by the Failure Criterion in Section 2.0.
From the definition of material properties used in the disk burst test, the uniform elongation for 304 stainless steel was 54% (see Section 3.0). Therefore, the failure of the disk will occur when the through-wall total strain exceeds 54% throughout the thickness.
An examination of the 3 geometries for both the axisymmetric and 3-D modeling can be seen in Figures 14 though 19. The results are further summarized in Table 3.
Table 3 Failure Criteria Comparison Model Model Failure Pressure psi)
Type Geometry Burst Test (31 Instability Failure Criteria Axisymmetric A
15000 14005
-11000 Axisymmetric B
6800 6694
-5500 Axisymmetric C
7700 6997
-5750 3-Dimensional A
15000 13997
-11000 3-Dimensional B
6800 6671
-5500 3-Dimensional C
7700 6974
-5750 Revision Preparer/Date RLB 5/31/02 Checker/Date File No. W-DB-0 IQ-304 Page 7 of 28 PRELIMINARY
PRELIMINARY 8.0 Conclusions Based on the summary in Table 3 of Section 7.0, the use of the uniform elongation limit as the basis of failure criteria in an elastic-plastic finite element analysis results in conservative failure pressures as compared to actual test results. For the three geometries, the uniform elongation criteria predicted a failure pressure that was in the range of 73% to 84% of the actual failure pressure.
A better prediction of actual failure pressure is the pressure at which numeric instability was reached in the ANSYS program. Assuming a numeric instability criterion, failure pressure would range from 90% to 98% of actual failure pressure.
PRELIMINARY 9.0 References
- 1) Structural Integrity Calculation W-DB-O1Q-301, Rev. 1, "Elastic-Plastic Finite Element Stress Analysis of Davis-Besse RPV Head Wastage Cavity."
- 2) Email of from B.R. Grambau (Framatome ANP) to N. Cofie (SI), "308 Stress -Strain Curve," March 15, 2002, SI File W-DB-01Q-202.
- 3) P. C. Riccardella, "Elastic-Plastic Analysis of Constrained Disk Burst Tests," ASME Paper No. 72-PVP-12, Proceedings of Pressure Vessel and Piping Conference, New Orleans, LA, September 17-21, 1972.
- 4) ANSYS/Mechanical, Revision 5.7, ANSYS Inc., December 2000
PRELIMINARY
-STRAIN-GAGED CANTILEVER BEAM FOR CENTRAL DEFLEC TION MEASLPEMENT SCHEMATIC ILLUSTRATION OF TEST SETUP DISK SPECIrEN 1Oin
"'THICKNESS FILLET GEOMETRY (I)
RADIUS A
025in 0 375 in B
0125 in.
0 125in C
0125 in 0 375 in Figure 1 - PVRC Disk Test Details (Reference 3) 0255RO
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PRELIMINARY
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4 Element Through-Wall
.1 6 Element Through-Wall Figure 4 - Mesh Density Example for 3-D Finite Element Model for Geometry-A
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V Preparer/Date RLB 5/31/02 Checker/Date File No. W-DB-01 Q-304 Page 14 of 28 PRELIMINARY
PRELIMINARY 11111111111111 a;
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Applied Pressure/
Figure 6 - Applied Pressure Example (Axisymmetric Geometry-A Model)
Revision 0
Preparer/Date RLB 5/31/02 Checker/Date File No. W-DB-01Q-304 Page 15 of 28 II:
liii II IT Ti PRELIMINARY II I
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PRELIMINARY Mesh Refinement vs. Onset of Numeric Instability Pressure 15000 14000 13000 12000 C' 11000 I 10000 2
- 10.
9000 8000 7000 6000 6
7 8
9 Through-Wall Element Counl Figure 7 - Mesh Density Effects 10 11 12
--- Axi-Geometry-Aj_
a-Axi-Geometry-B
"--*-Axi-Geometry-C
-*-3D-Geometry-A
--*-3D-Geometry-B
-*--3D-Geometry-C 4
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PRELIMINARY Revision V
Preparer/Date RLB 5/31/02 Checker/Date File No. W-DB-OIQ-304 Page 17 of 28 Von Mises Tota ANSYS 5.7 MAY 22 2002 08:48.09 PLOT NO.
1 NODAL SOLUTION STEP=1 SUB =50 TIME=.33654 EPTOEQV (AVG)
EffNui-0 DMX =2.352 SMN =.472E-03 SMX =1.216
.472E-03
.135477
.405487
.540492
.675497 r 1.810503
.945508 1.081 1.216 al Strain (12x96)-
(Category-A)
Figure 8 - Total Von Mises Strain Just Prior to Numeric Instability Geometry-A - Axisymmetric
PRELIMINARY ANSYS 5.7 MAY 22 2002 08:20:47 PLOT NO.
I NODAL SOLUTION STEP=1 SUB =50 TIME=A.4'627 EPTOEQV (AVG)
EffNu=0 DMX =2.35 SM
=.183E-03 SMX =1.407
"-
183E-03 A156501 m~ 312819
.469136
.625454
)
.781772
.938089 m*1.094 m 1.251 1.407 Von Mises Total Strain -
(12x96) -
(Category B)
Figure 9 - Total Von Mises Strain Just Prior to Numeric Instability Geometry-B - Axisymmetric Revision 0
Preparer/Date RLB 5/31/02 Checker/Date
ANSYS 5.7 MAY 22 2002 08:26:25 PLOT NO.
1 NODAL SOLUTION STEP=-1 SUB =43 TIME=.466474 EP¶OEQV (AVG)
EffNu=O DMX =2.263 SMN =.206E-03 SMX =1.218 I.206E-03 I.135536
.270865
.406195 I.41524 M
.676854 S.812183
.947513 1.083 1.218 Von Mises Total Strain -
(12x96) -
(Category-C)
Figure 10 - Total Von Mises Strain Just Prior to Numeric Instability I Geometry-C - Axisymmetric
PRELIMINARY Von Mises Total Strain -
(6x48) -
(Category-A)
Figure 11 - Total Von Mises Strain Just Prior to Numeric Instability Geometry-A Dimensional ANSYS 5.7 MAY 22 2002 09:01'11 PLOT NO.
1 NODAL SOLUTION STEP=1 SUB =26 TIME=.933132 EPTOEQV (AVG)
EffNu=0 TOP DMX =2.296 SMN =.277E-03 SMX =1.167
.277E-03
-129911
.259545
.389178
.518812 a0.648446
.778079
.907713 1.037 1.167
PRELIMINARY Figure 12 - Total Von Mises Strain Just Prior to Numeric Instability Geometry-B Dimensional Revision 0
Preparer/Date RLB 5/31/02 Checker/Date File No. W-DB'-01Q-304 Page21of8 Von Mises Total Strain - (6x48) -
(Category-B)
ANSYS 5.7 MAY 22 2002 09:09:37 PLOT NO.
I NODAL SOLUTION STEP=-1 SUB =30 TflE=.444724 EPTOEQV (AVG)
EffNu=O TOP DMX =2.245 SMN =.112E-03 SMX =1.353
.112E-03
.150391
.300669
.450947
-m.601225
.751503
.901781
-1.052
-1.202 1.353
PRELIMINARY Revision 0
Preparer/Date RLB 5/31/02 Checker/Date File No. W'-DB-01Q-304 Pag*e 22 of 28 Von Mises Tot ANSYS 5.7 MAY 22 2002 09:14:07 PLOT NO.
1 NODAL SOLUTION STEP=-1 SUB =28 TIME=.464911 EPTOEQV (AVG)
EffNu=0 TOP DMX =2.157 SMN =.I14E-03 SMX =1.113 i
.114E-03 i
.123754 247393 S.,371032
.494672
.618311
___.74195
.86559
.989229 1.113 al Strain-(6x48) - (Category-C)
Figure 13 - Total Von Mises Strain Just Prior to Numeric Instability Geometry-C Dimensional
PRELIMINARY Pressure vs Total Von Mises Strain at Center Geometry-A (Axisymmetric) 0.2 0.4 0.6 0.8 1
1.2 Total Von Misas Strain (inlin)
Figure 14 - Through-Wall Strain Results at Center of Disk Geometry-A (Axisymmetric) 16000 Test Burst Pressure = 15,000 psi
- u-.*.-P -*. *............
i...........................................................
14000 12000 10000 8000 6000 0
- 0.
U U
0
4000 2000 0
0 1.4
Pressure vs Total Von Mises Strain at Center Geometry-B (Axisymmetric) 7000 Tes'tBurst*Pre~s'sure =_ 6.800 psi 6000 5000 3000..
To0al VD-Middle 2O0
/.,*
- ,w.-l-Bottom 0
0.2 0.4 0.6 0.8 1
Total Von Mises Strain (in/in)
Figure 15 - Through-Wall Strain Results at Center of Disk Geometry-B (Axisymmetric) 1.2
PRELIMINARY Pressure vs Total Von Mises Strain at Center Geometry-C (Axisymmetric) 8000 7000 6000 5000 4000 S3000 2000 1000 0
0 0.2 0.4 0.6 0.8 Total Von Mises Strain (Inrin)
I
_I_
1 1.2
-J Figure 16 - Through-Wall Strain Results at Center of Disk Geometry-C (Axisymmetric)
Revision 0
Preparer/Date RLB 5/31/02 Checker/Date File No. W-DB-01 Q-304 Page 25 of 28 Test Burst Pressure = 7,700 psi
PRELIMINARY Pressure vs Total Von Mises Strain at Center Geometry-A (3-Dimensional) 0 0.2 0.4 0.6 0.8 Total Von Mises Strain (infln)
Figure 17 - Through-Wall Strain Results at Center of Disk Geometry-A (3-Dimensional) 1 Test Burst Pressure = 15,000 psi
.o..................
.. o.... o.................P
°........................................
0.
16000 14000 12000 10000 8000 6000 4000 2000 0
1.2 I
PRELIMINARY Pressure vs Total Von Mises Strain at Center Geometry-B (3-Dimensional) 0 0.2 0.4 0.6 0.8 1
Total Von MIses Strain (imlin)
Figure 18 - Through-Wall Strain Results at Center of Disk Geometry-B (3-Dimensional)
Tet
............ u s............... e.......6......
T...e-st Burs-t P.re~s~s~ure.=. 6.600. -psi i
7000 6000 5000 4000 f 3000 2000 1000 0
1.2
PRELIMINARY Pressure vs Total Von Mises Strain at Center Geometry-C (3-Dimensional) 0.2 0.4 0.6 0.8 1
1.2 Total Von Mises Strain (Infln)
Figure 19 - Through-Wall Strain Results at Center of Disk Geometry-C (3-Dimensional)
"Tet urt resue 7.700", p IW 0.
I 0
J 8000 7000 6000 5000 4000 3000 2000 1000 0
PRELIMINARY APPENDIX A
NRC Staff Comments and Ouestions on Davis-Besses Safety Significance Assessment (SIA-W-DB-010-301) Submitted April 8. 2002
PRELIMINARY NRC STAFF COMMENTS AND QUESTIONS ON DAVIS-BESSE SAFETY SIGNIFICANCE ASSESSMENT (SIA-W-DB-01Q-301) SUBMITTED APRIL 8,2002 FAILURE CRITERION (1)
What is the technical basis of the failure criterion (e.g., strain exceeding 11.15%) used to determine the failure conditions of the cladding layer? Provide specific technical references in the literature that support the failure criterion used in this evaluation.
(2)
How does the failure criterion (e.g., based on ultimate strain in a uniaxial tensile test) account for the effects of biaxial loading in the cladding, or triaxial loading in the cladding at the edges of the degradation cavity?
(3)
The failure criterion applied in SIA report W-DB-01 0-301 (e.g., the minimum cross sectional strain exceeding the failure strain of 11.15%) allows the strain levels in the cladding to exceed the critical strain value entirely through the thickness, leading to very large strains at the surface of the cladding, up to 49% in Table 5 of the SIA report. What is the technical basis for this approach, as opposed to the average cross-sectional strain, or the maximum cross-sectional strain?
(4)
Did you explore a continuum damage mechanics analysis to give guidance of the failure criterion once the strains exceed the critical strain where necking/void growth starts? If not, provide the technical basis for not using a continuum damage mechanics analysis.
[Poisson's ratio of 0.5 no longer applies once this critical strain level is exceeded, so the analysis is strictly not valid. (Poisson's ratio is continuously changing as the voids grow at the strains beyond the start of necking.) This results in a stress redistribution that is not accounted for in a standard elastic-plastic analysis.]
(5)
How would the strain values change if the stress free temperature was assumed to be the stress relief temperature instead of 700F, and the analysis accounted for the differential thermal expansion of the cladding and head steel at the operating temperature of 6050 F?
GEOMETRY/MESHING (A)
Does the size of the degradation cavity and the transition from the cladding thickness to the head thickness that was used in the SIA report reflect current knowledge regarding the cavity geometry, in particular the undercut area described in Figure 13 on page 103 of the Davis-Besse Root Cause Analysis Report (CR2002-0891), dated April 15, 2002? What is the transition geometry assumed in the analyses?
(B)
Is there sufficient mesh refinement through the cladding thickness to adequately capture the bending and shear strains at the edge of the cavity? Describe any sensitivity studies used to demonstrate the adequacy of the mesh refinement.
(C)
Was the cladding deposited by weld wire? Do the thinner cladding thickness measurements from UT coincide with the locations of weld bead toes? In what direction do the cladding weld beads run relative to the long axis of the degradation cavity?
APPENDIX B
Pressure Vessels and Piping Division Paper No. 72-PVP-I 2, "Elasto-Plastic Analysis of Constrained Disk Burst Tests"