ML021990457
| ML021990457 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse  |
| Issue date: | 07/12/2002 |
| From: | Bergendahl H FirstEnergy Nuclear Operating Co |
| To: | Dyer J NRC/RGN-III |
| References | |
| 1-1280 | |
| Download: ML021990457 (49) | |
Text
FENOC FirstEnergy Nuclear Operating Company Howard W. Bergendahl 41 Vice President - Nuclear Fax: 41 Docket Number 50-346 License Number NPF-3 Serial Number 1-1280 July 12, 2002 Mr. James E. Dyer, Administrator United States Nuclear Regulatory Commission Region III 801 Warrenville Road Lisle, IL 60532-4351
Subject:
Confirmatory Action Letter: Response to Request for Additional Information Related to the Davis-Besse Nuclear Power Station Safety Significance Assessment
Dear Mr. Dyer:
This letter responds to the June 24, 2002 (Log Number 5980) NRC staff request for additional information (RAI) related to the Safety Significance Assessment of the Davis-Besse Nuclear Power Station (DBNPS) Reactor Pressure Vessel Head as was submitted by FirstEnergy Nuclear Operating Company letter Serial Number 1-1268 dated April 8, 2002. The RAI included questions from the Office of Nuclear Reactor Regulation and the Office of Nuclear Regulatory Research.
Should you have any questions or require additional information, please contact Mr. Patrick J. McCloskey, Manager - Regulatory Affairs, at (419) 321-8450.
Very truly yours, MKL Enclosures
'ThQ2
'2. 1,tAQ
Davis-Besse Nuclear Power Station 5501 North State Route 2 Oak Harbor, Ohio 43449-9760 9-321-8588 9-321-8337
Docket Number 50-346 License Number NPF-3 Serial Number 1-1280 Page 2 cc:
USNRC Document Control Desk D. V. Pickett, NRC/NRR Project Manager S. P. Sands, NRC/NRR Backup Project Manager C. S. Thomas, NRC Region III, DB-1 Senior Resident Inspector Utility Radiological Safety Board
Docket Number 50-346 License Number NPF-3 Serial Number 1-1280 Page 1 RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION REGARDING THE APRIL 8, 2002 SAFETY SIGNIFICANCE ASSESSMENT FOR DAVIS-BESSE NUCLEAR POWER STATION UNIT NUMBER 1 FAILURE CRITERION Question 1:
What is the technical basis of the failure criterion (e.g., strain exceeding 11.15 percent) 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.
DBNPS Response to Question 1:
The strain value of 11.15% corresponds to the uniform elongation of the stress-strain curve used in the evaluation. The use of this value as the basis for the failure criterion is based largely on engineering judgment. The premise is that when any section in the cladding has through-wall strains greater than the uniform elongation, then that section has no more capacity of resisting any additional increase in load. This criterion is judged to be conservative because in reality, there is redistribution of stresses and strains to adjacent elements that would prevent incipient failure when the strains in a particular column of elements exceed this criterion.
Furthermore, it should be noted that the value of uniform elongation used in the evaluation (11.15%) is very conservative for stainless steel weld metal. Data obtained from the literature, and summarized in Table 1 indicates that the average unifonrm elongation for submerged arc welds (SAW) is 25.7% and that for shielded metal arc welds (SMAW) is 30.7%. The average for both populations is 27.3%. Most of the data shown in Table 1 indicate unifoma elongation greater than 20% with only two data points below this value.
Subsequent to the publication of Structural Integrity report W-DB-OIQ-301 (Reference 1), an evaluation of the reasonableness of the failure criterion was performed, W-DB-0IQ-304 (Reference 2), using disk burst test data (Reference 3). A copy of the evaluation is attached. The disk burst test data is included as Appendix B to the evaluation. The conclusion of the evaluation is that the failure criterion is conservative compared to the disk burst test results. The burst test pressures were also compared to the pressures at which numerical instability occurred
Docket Number 50-346 License Number NPF-3 Serial Number 1-1280 Page 2 during the elastic-plastic analysis and it was found that the instability pressures, although slightly under-predicting the test failure pressures, are a much better predictor of failure pressure than any of the proposed strain-based failure criteria.
Base on the above information and data, it is believed that the use of the 11.15% uniform elongation as a basis for the failure criterion is very conservative.
Docket Number 50-346 License Number NPF-3 Serial Number 1-1280 Enclosure I Page 3 Table 1: Tensile Test Data for 304 Stainless Steel at 550 'F Yield Ultimate Uniform Reduction Reference Strength Tensile Strength Elongation in Area Material (ksi)
(ksi)
(%)
(%)
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 NUREG/CR-4687 20.1 65.2 53.8 71.3 Base EPRI 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 72PVP12 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 47.1 67.6 31.5 44.2 SAW NUREG/CR-4878 28.3 67.5 34.5 47 SAW Annealed 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 Ave.SAW&SMAW 27.3 53.8
Docket Number 50-346 License Number NPF-3 Serial Number 1-1280 Page 4 Question 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?
DBNPS Response to Question 2:
The failure criterion was based solely on the uniform elongation and did not consider biaxial or triaxial effects. Nevertheless, as discussed in the response to Question 1, the criterion is conservative compared to burst test results on test specimens that are similar to the exposed cladding in the degradation cavity geometry.
Question 3:
The failure criterion applied in Structural Integrity Analysis (SIA) report W-DB-OIQ-301 (e.g.,
the minimum cross-sectional strain exceeding the failure strain of 11.15 percent) 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 percent 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?
DBNPS Response to Question 3:
Even though the failure criterion used resulted in some elements in the cross-section exceeding the failure strain, the criterion, as compared to actual burst test data, was found to be conservative (see response to Question 1).
Question 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.]
Docket Number 50-346 License Number NPF-3 Serial Number 1-1280 Page 5 DBNPS Response to Question 4:
The analysis performed was judged to be conservative as validated by the disk burst test results discussed in the response to Question 1, and as such, it was judged unnecessary to consider the application of continuum damage mechanics analysis to this evaluation.
Question 5:
How would the strain values change if the stress free temperature was assumed to be the stress relief temperature instead of 70 'F, and the analysis accounted for the differential thermal expansion of the cladding and head steel at the operating temperature of 605 'F?
DBNPS Response to Question 5:
As can be seen in the Structural Integrity report W-DB-0 1Q-301, and as further clarified by the above responses to Questions 1 through 4, the strains at the failure pressures from both the analyses and experiments are very large (on the order of 1 1% or greater). The strains corresponding to thermal expansion effects, at either temperature, are expected to be much smaller (on the order of 0.1%). Therefore, the effects of changing from a stress free temperature of 70 'F to 605 'F will not have any significant impact on the results of the analysis.
GEOMETRY/MESHING Question 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 (CR 2002-0891), dated April 15, 2002? What is the transition geometry assumed in the analyses?
DBNPS 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 detennine the exact size and geometry of the cavity and 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.
Docket Number 50-346 License Number NPF-3 Serial Number 1-1280 Enclosure I Page 6 Response to Question B:
In the analysis of the 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 categories with six elements though 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 ultrasonic testing 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?
DBNPS 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 cavity is currently in progress that might provide more information.
References
- 1)
Structural Integrity Calculation W-DB-01Q-301, Rev. 1, "Elastic-Plastic Finite Element Stress Analysis of Davis-Besse RPV Head Wastage Cavity."
- 2)
Structural Integrity Calculation W-DB-01Q-304, Rev. 0, "Evaluation of Failure Criterion Used in Elastic-Plastic Analysis of Davis-Besse RPV Wastage."
- 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.
Docket Number 50-346 License Number NPF-3 Serial Number 1-1280 Attachment Structural Integrity Calculation W-DB-01 Q-304 (39 pages attached)
- P STRUCTURAL CALCULATION FILE No: W-DB-O1Q-304 INTEGRITY Associates, Inc.
PACKAGE PROJECT No: W-DB-01Q 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
- ./3 g"/o o
BI -B9 Project CD-Rom (I
"7" "
PAGE 1
of 28
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 1 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 ABS-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.
Revision 0
SPreparer/Date RLB 6/25/02 FieN.WD-l-34Pg f2 Page 2 of 28 File No. W-DB-0 1Q-304
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:
28.3 Poisson's Ration, v:
0.3 The plastic material properties for stainless per Reference 3 were:
0.25 Y.S.
suit F ult Reduction Al]1 (psi)
(psi)
(in/in)
In Area (psi) 34,000 84,000 0.54 0.74 193,060 0.494
[1] Stress Strain Curve Assumed to be of form a = A (s) '
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.
Revision 0
Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02 File No. W-DB-0 Q-304 Page 3 of 28
Table 1 Stress Strain Curve for 304 Stainless Steel [3]
Strain (in.in)
Stress (psi) 0.000 0
0.025 31208.63 0.050 43952.49 0.075 53699.79 0.100 61900.24 0.125 69113.97 0.150 75627.79 0.175 81611.83 0.200 87176.84 0.225 92399.68 0.250 97336.26 0.275 102028.8 0.300 106510 0.325 110805.8 0.350 114937.5 0.375 118922.4 0.400 122775 0.425 126507.5 0.450 130130.6 0.475 133653.1 0.500 137083 0.525 140427.1 0.550 143691.6 0.575 146881.9 0.600 150002.7 0.625 153058.4 0.650 156052.8 0.675 158989.5 0.700 161871.6 0.725 164702.2 0.750 167483.7 0.775 170218.7 0.800 172909.5 0.825 175558 0.850 178166.2 0.875 180735.8 0.900 183268.6 0.925 185766 0.950 188229.5 0.975 190660.4 1.000 193060 1.025 195429.4 1.050 197769.7 1.075 200082 1.100 202367.3 1.125 204626.4 1.150 206860.2 1.175 209069.7 1.200 211255.4 1.225 213418.2
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 be the portion of the disk that 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 300 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 [1] 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, symmetric boundary conditions were applied to the outside radial section surface 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 instability was reached. See Figure 6 for an example of the applied pressure.
Revision 0
Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02
_ File No. W-DB-OIQ-304 Page 5 of 28
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 thirough-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 0
Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02 File No. W-DB-0 IQ-304 Page 7 of 28
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 81% of the actual failure pressure.
A better prediction of actual failure pressure is the pressure at which instability was reached in the ANSYS program. Assuming a instability criterion, failure pressure would range from 90% to 98% of actual failure pressure.
Revision 0
V Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02 File No. W-DB-O1Q-304 Page 8 of 28 I
9.0 References
- 1) Structural Integrity Calculation W-DB-01Q-301, Rev. 1, "Elastic-Plastic Finite Element Stress Analysis of Davis-Besse RPV Head Wastage Cavity."
March 15, 2002, SI File W-DB-O1Q-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
- 5) ASME Boiler and Pressure Vessel Code,Section II, Part D, 1998 Edition Revision Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02 File No. W-DB-OIQ-304 Page 9 of 28
STRAIN-GAGED CANTILEVER BEAM FOR CENTRAL DEFLEC TION MEASUREMENT r
L 1
APPLIED PRESSURE SCHEMATIC ILLUSTRATION OF TEST SETUP DISK SPECIMEN 1.0 in.
Figure 1 - PVRC Disk Test Details (Reference 3)
Revision 0
Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02 1
File No. W-DB-0 1Q-304 Page 10 of 28 THICKNESS FILLET GEOMETRY (t)
RADIUS A
0.25 in.
0.375 in.
B 0.125 in.
0.125in.
C 0.125 in.
0.375in.
02055RO
4 Element Through-Wall 8 Element Through-Wall 12 Element Through-Wall Figure 2-Mesh Density Example for Axisymmetric Finite Element Model for Geometry-A Revision Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02 File No. W-DB-O1Q-304 Page 11 of 28
IF III 1 1 7 1TV1V1 VVV I 1 1
¶
? !.
1 F 3
.t. f
-H
- - -tV-
//i1
'1 fT 1
1 1 -I-.--
Figure 3 - Mechanical Boundary Conditions Example for Axisymmetric Finite Element Model for Geometry-A Revision Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02 File No. W-DB-O1Q-304 Page 12 of 28
-7 1
1 1
__*__L__'.__E__L__L__2__l__L__I__I__.
__1 *_ I
[
.' __I ]--l-
- --I
.!--I--J l
J 1....
",t J[*][*Jl ¢ I 4'! ;,, 1 0,,
. ý, 1-1Q
",,'P,. * ° t,,',,*,,',,* '.
4 Eloiient ro'Ilri-V',II 6 E lemnent Th rou. 1,1 -Wa-llI Figure 4 - Mesh Density Example for 3-D Finite Element Model for Geometry-A
Figure 5 - Mechanical Boundary Conditions Example for 3-D Finite Element Model for Geometry-A Revision Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02 File No. W-DB-O1Q-304 Page 14 of 28
A,/
///
Applied Pressure' Figure 6 - Applied Pressure Example (Axisymmetric Geometry-A Model)
Revision0 Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02
_File No. W-DB-O lQ-304 Page 15 of 28
Mesh Refinement vs. Onset of Numeric Instability Pressure Axi-Geometry-A1
--- Axi-Geometry-B I_ -
Axi-Geometry-C 3D-Geometry-A
-- 1
--. 3D-Geometry-C 7
8 9
Through-Wall Element Count 10 11 File No. W-DB-01 Figure 7 - Mesh Density Effects 0
ýLB 6/25/02 3ST 6/25/02 Q-304 Page 16 of 28 15000
- 14000, 13000 12000 CL 11000 10000-9000 8000 7000 6000 F
-
4 5
6 12 i'~~~
.b' I
Co I
C-03
LJ() 3
co&
0
0 Pressure vs Total Von Mises Strain at Center Geometry-A (Axisymmetric)
I UUU 14000 12000 10000 8000 6000 4000 2000 0
0 0.2 0.4 0.6 0.8 1
1.2 Total Von Mises Strain (Intin) 1.4 Figure 14 - Through-Wall Strain Results at Center of Disk Geometry-A (Axisymmetric)
Revision 0
Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02 File No. W-DB-O1Q-304 Page 23 of 28
Pressure vs Total Von Mises Strain at Center Geometry-C (Axisymmetric)
Pressure. = 7.700 psi' 0.2 0.4 0.6 0.8 Total Von Mises Strain (!ntln) 1 Figure 16 - Through-Wall Strain Results at Center of Disk Geometry-C (Axisymmetric) 8000 7000 6000
-5000 S4000 m
Af 2000 1000 0
0 129
- uuu 1 2
Pressure vs Total Von Mises Strain at Center Geometry-A (3-Dimensional) 16000 14000 12000 2=
10000 8000 6000 4000 2000 0
0 0.2 0.4 0.6 0.8 1
1.2 Total Von Mises Strain (in/in)
Figure 17 - Through-Wall Strain Results at Center of Disk Geometry-A (3-Dimensional)
Revision Preparer/Date RLB 6/25/02 Checker/Date SST 6/25/02 File No. W-DB-01Q-304 Page 26 of 28 Test Burst Pressure = 15,000 psi
~
Pressure vs Total Von Mises Strain at Center Geometry-C (3-Dimensional) 8000...t
' u i s u
,Y " i........ !.....................................
Test Burst Pressure =7,700 psi...............
7000 6000
, 5000 3000 2000 *//-i Bottom CIO 300 oTo 0
0.2 0.4 0.6 0.8 Total Von Mises Strain (inlin)
Figure 19 - Through-Wall Strain Results at Center of Disk Geometry-C (3-Dimensional)
I 1.2
APPENDIX A
NRC Staff Comments and Ouestions on Davis-Besses Safety Sianificance Assessment (SIA-W-DB-01Q-301) Submitted April 8, 2002 Revision Preparer/Date RLB 5/31/02 Checker/Date File No. W-DB-OIQ-304 Page Al of A2
NRC STAFF COMMENTS AND QUESTIONS ON DAVIS-BESSE SAFETY SIGNIFICANCE 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-01Q-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 70°F, and the analysis accounted for the differential thermal expansion of the cladding and head steel at the operating temperature of 6050F?
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?
Revision 0
Preparer/Date RLB 5/31/02 Checker/Date File No. W-DB-O1Q-304 Page A2 of A2
APPENDIX B
Pressure Vessels and Piping Division Paper No. 72-PVP-12, "Elasto-Plastic Analysis of Constrained Disk Burst Tests" Revision 0
VPreparer/Da RLB 5/31/02 Checker/Date File No. W-DB-O1Q-304 Page BI of B9
Elasto-Plastic Analysis of Constrained Disk Burst Tests The PVRC Subcommittee on Effective Utilization of Yield Strength has conducted an extensive series ofpressurized burst tests on constrained disk specimens of seven steels.
Elasto-plastic analyses have been performed for nine of these tests and the results are presented in this report. Good agreement between the analytical and experimental results all the way to failure pressure is illustrated by a comparison of centerline de flections. Interpretation of the analytical data indicates that both edge type and center line type offailures are correlated reasonably well by the conventional reduction in area from a uniaxial tensile test once triaxiality is accounted for.
Introduction THE PVRC Subcommittee on Effective Utilization of Yield Strength has conducted a series of constrained disk burst tests [1(] using the disk specimen and test setup illustrated in Fig. 1. In order to interpret these tests and their relation to the safety margins which exist in the components of a Westing house nuclear steam supply system, elasto-plastic analyses have been performed on three disk geometries with three materials each.
The three materials considered were type 304 stainless steel, ASTM A533B low-alloy steel, and ABS-C carbon steel.
These materials are representative of reactor core support struc tures and piping, the reactor pressure vessel, and plant com ponent supports, respectively.
A summary of the mechanical properties from uniaxial tensile tests performed on the actual disk materials is given in Table 1.
Extensive data from the disk tests, including burst pressures and experimental pressure versus deflection curves have been reported in references [1] and [21.
Some of the disks failed at the disk centerlines, while others failed along the edge of the disks at the fillet between the thin and thick regions.
Table 2 sum marizes the failure data for the disks considered in this analysis, which include three centerline failures and six edge failures.
The details of the three disk geometries are tabulated in Fig. 1.
1Numbers in brackets designate References at end of paper.
ontributed by the Pressure Vessels and Piping Division for presentation at the Petroleum Mechanical Engineering Conference With Pressure Vessels and Piping Conference, New Orleans, La.,
September 17-21, 1972? of THE AmSrIc.AN SOCIETY OF MECHANICAL EiorNE*.suS.
Manuscript received at ASME Headquarters, June 6, 1972. Paper No. 72-PVP-12.
Copes will be available until June, 1973.
-STRAIN-GAGED CANTELEVER BEAM FOR CENTRAL DEFLEC T
lION MEASUREMENT
"-APPLIED PRESSUR]E
-SCHEMATIC ILLUSTRATION OF TEST SETUP DISK SPECIMEN X
r4 1.0I
-6.0 IN
- 10.
- 0. IN THICKNESS FILLET (t)
RADIUS (r)
A
- 0. 25 IN
- 0. 375 IN B
- 0. 125 IN
- 0. 125 IN C
0.125 IN
- 0. 375 IN Fig. 1 PVRC disk test delails I
Discussion on this paper will be accepted at ASME Headquarters until October 23, 1972 P. C. RICCARDELLA Materials and Stress Analysis, Westinghouse Nuclear Energy Systems, Pittsburgh, Pa.
Table 1 Material properties Material
.2' Y.S.
Sult.
Cult.
Reduction A'
n' (PSI)
(PSI)
(In/in) in area (PSI)
Type 304 Stainless 34,000.
84.000.
.54
.74 193,060.
.494 Steel A-5338 LowAlloy 74.000.
96.000.
.17
.68 146,000.
.141 Steel Cabon 39,000.
84,000.
- 31
.66 115,130.
.242 Steel
- Stress-strain curve assuned to be of form o - A cn Table 2 Experimental failure data Burst Type of Materi a II Geametry Pressure (PSI)
Fa i Iure 304 S.S.
A 15,000.
Edge B
6,800.
Center C
7,700.
Center A-$33 3 A
11,000.
Edge B
5,300.
Edge C
6,700.
Center ABS-C A
9,800.
Edge B
3,750.
Edge C
4,940.
Edge 4 UU I. 75 1,50
.255 I 00 0.15 050 0 25 0,00 0 304-SS 5000 10,000 PRESSURE (PSI) 15,000 Fia. 3(a)
PVRC disk lests-centerline deflectionversus pressure (experi mental and analytical results for 304 stainless steel disks)
A-533 8 I5-GEOMETRY B 10 Os 0 6 -
GEOMETRY A
0 4-EXPERIMENTAL
/
0---0 ANALYTICAL i GAPL) 00 L-- -"
O -//-*
5000 10, 000 15.000 PRESSURE (PSI, Fig. 3(b)
PVRC disk tests-centerline deflection versus pressure (ex perimental and analytical results for A-533 B low alloy steel disks) a.) GAPL MODEL OF GEOMETRY A 02
- b. ) GAPL MODEL OF GEOMETRY B
- 4 -f, -ý- -I- -÷ - -; -
=+ý-ý II -t' -- -I-
ý +
--:j-z Z T
t -- 0.125 IN.
r = 0.375 1 V c.) GAPL MODEL OF GEOMETRY C Fig. 2 Computer models of PVRC disks Anatysfs The analysis of the disks was performed using the computer program GAPL-3
[31.
This program performs elasto-plastic, large-deformation analysis for stresses, strains, loads, and de flections of thin plates or axially symmetric shells with pressure loading and deflection restraints.
The discrete element method employed in GAPL-3 requires fewer elements than conventional finite element techniques to adequately describe structures with high stress gradients because it makes use of a two-layered system of elements:
one layer for the strain-displacement field, and a second layer for the stress field. The body is first divided into constant thickness, finite length strain-displacement elements 2
15,000 PRESSURE (PSI)
Fig. 3(c)
PVRC disk tesls-centerline deflection versus pressure (experi mental and analytical results for ABS-C carbon steel disks)
Fig. 3 along the axis of the body.
The deflections in the elements are represented by a bending type polynomial along the axis and by a linear variation through the thickness.
Each element is then further subdivided into constant stress regions in which the stresses are found as a function of the strains in the region.
It is the deflection elements, however, which dictate the size of the problem.
The pressure loading is applied in steps and an equilibrium solution is found at each step by iterating for both geometric and material nonlinearities.
The choice of incremental or deforma tion theory of plasticity is made by the user according to the size of the load steps he chooses.
Since the program must iterate at each load step, the finer the load steps, the more costly the prob lem becomes.
Transactions of the AS ME 25 1,!
304-SS 5003 10.000 PRFSSIJRF (plM!
2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00
!5000 1.50 1.25 I.00
- 0. 75 0.50 0.25 0.00 GEOMETRY C
EXPERIMENTAL 0-- -- ANALYTICAL (GAPL) 5003 0.000 PRESSURE (PSI)
Fig. 4(c)
PVRC disk fests-centerline deflection versus pressure (ex perimental and analytical results for ABS-C carbon steel disks)
Fig. 4 1.2 1.0 0.8 0.6 0.4 A-533GOER C
10,000 Table 3 Strain concentration factors K.it.r.
a I Exponent!
...o ry A I G v....y B f.eometry c
r K
./r (n)3 W5 1 1 7 P1..
GAP rA GAO K1..PL V GA PL 3387!
7.2
.98
.5
.94
.0
.86, ABS-C i 304 -. S i
.242
.494 4.1 2.0 5.3 3.6
.77
.56 6.1 4.5
,6'
..38 15,000 PRESSURE (PSD Fig. 4(b)
PVRC disk tests-centerline deflection versus pressure (ex perimental and analytical results for A-533 B low alloy steel disks)
T'he three FVR-C disk geometries were represented by the discrete strain-displacement element models shown in Fig. 2 In the thin portion of the disks eight stlre-ss regions were specified for each strain-displacement element, while in the filet regions twelve stress regions per element were used.
Material properties for the three steels analyzed were input interms ofa powerhard ening law, using the cnnstantsA and n listed m Table I. Both fine and crude load steps were tested to evaluate the effect of de formation versus incremental theories of plasticity, and the re suits were practically identical which indicates that the problem is a proportional loading situation.
The production runs were then made tuing five lbad'steps per case so that a reasonable representation of stresses and displacements as a function of applied pressure could be obtained.
Resuiis A comparison of the experimental and analytical centerline deflections at various pressures is given for geometries A and B in Fig. 3 and for geometry C in Fig. 4.
The agreement is ex cellent all the way to failure pressure in eight of the nine cases considered.
In the ninth case (ABS-C, geometry C) some diffi culty was experienced in getting convergence at high pressures, although the experimental-analytical agreement was good at low pressures.
In all cases the experimental data shows a tailing up as the pressure approaches burst pressure which the analytical results fail to predict.
Since the GAPL program does not ac count for reduction in thickness, it can not be expected to pre dict tensile instability which the experimental tailing up repre sents.
Since the analytical prediction of. centerline deflection was so good, it is expected that the stress and strain distributions pre dieted by GAPL are reasonable estimates of what occurred in the actual test specimens.
Some reservation is called for in the fillet region, however, since the thin shell approximations of the GAPL program are not strictly valid there.
The GAPL analysis includes plastic hinge type of strain redistribution, but the strain concentrationeffect due to fillet radius is not accounted for since the predicted strain distribution in the cross section of the fillet is linear there by :Ls tion.
As the ire increased, the computed stresses at the disk centerlines al)proached a state of uniform biaxial membrane stress with 1 l bendi stress.
In the fillet, the mem brane stresses were lower than at, the disk centerline, but t.he stresses on the inside surface of the fillet were the highest in the disk 6, and 7 summarize the computed stress and strain data for the fillet, and centerline regions of the disks for the 304 SS, the A-5333 13 and the ABS-C, respectively The curves give maximum valbes ofvon Mise.s equivafent stress and strain hi the two locations.
Severalauthors '
61 have noted that the strain concentra tion (or redistribution) in the fillet in tests such as this should iTi creme as the strainhardening exponent (nl ecreases. As a first approximation, use of a strain concentration factor (K,)which is inversely proportional to n has been suggested [71.
In Fig. 8, the maximum radial fillet strains from the GAPL analysis have been cross-plotted against centerline deflections from Figs. 3 and 4 in order to study the effect of hardening exponent upon strain redistribution.
The trend of increasing strain concentration with decreasing strain hardening is evident in this figure for all three geometries.
A simple elastic analysis has been performed on the disks in order to test the simple inverse proportion rule mentioned previ ously.
The resulting maximum stresses in the fillet have been divided by Young's modulus and the results are given by the elastic lines in Fig. 8. Strain concentration factors have been computed at three discrete values of centerline deflection (0.6 in.,
0.8 in., and 1.0 in.) by dividing the strains from the elasto-plastic GAPL analysis by the elastically computed strains at each de flection.
The resulting strain concentration factors were then averaged over the three deflections, and these average values are listed in Table 3. This table shows that while the (1/0) approxi mation is quite good for the lowest strain hardening exponent (n = 0.141), it tends to get worse as n increases.
The inverse Journal of Engineering for Industry (A
z 0
Fig. 4(a)
PVRC disk tests-centerline deflection versus pressure (experi mental and analytical results for 304 stainless steel disks) 15,000 GEOMETRY C
F~0 O----< AN PERIMENTAL WALYTICAL
( GAPL
)
3 A-533 8
u.
0.2 0.0 0
160 1
I I
140 I
I I r 1 1 140 -
GEOMETRY A 120 -
FILLET GEOMETRY C 120 --
FILLET a,
O
~ 100~
soCENTER' 10 IO-
ý4 80 CENTER 6
BURST PRESSURE
)
80 -
60 C
(
60 40 40 BURST PRESSURE' 20 20 f 01 0.70 GEOMETRY C 0.80 1 0.60 GEOMETRY A 0.70 -
0.50 0.60-0.40
~FILLET
=2' 0.50 -
FIL I
030 -"
BURST PRESSURE z
0.40 -
- 0. 21)
</
CENTER V) 0.30 0.10 CT 0.20CENTER 1
- 0. O I
0.20 1
0 4000 8000 12,000 16,000 0.10 BURST PRESSURE; PRESSURE (PSI) 0.00 1
8 2 0
, 000 Fig. 5(c)
Stress and strain data for 304 stainless steel disks 0
4000 8000 12,.000 16, 000 PRESSURE (PSD Fig. 5 Fig. 5(a)
Sfress and strain data for 304 stainless steel disks proportion rule substantially underestimates the strain concen tration for the stainless steel disks (n = 0.494).
160 1
1 1 1 Interpretation of Results 140 --
FILLET I
GEOMETRY B I
An interesting interpretation of this work arises when the 120 -
equivalent strain levels at failure shown in Figs. 5, 6, and 7 are CENTER tabulated.
All of the edge failures occurred at approximately S100 the same strain level (*-.50 percent) and all of the centerline occurred at approximately the same strain level (.-'35 S
80 IBURST PRESSURE percent).
(See Table 4).
This seems surprising at first, since
)-
the ultimate or uniform strains for the three materials are 54 percent for the stainless steel, 17 percent for the low alloy sfeel, 40 and 31 percent for the carbon steel as indicated in Table 1.
However, the ultimate or uniform strain in a tensile test is some 20 what artificial as a material property since it is really a measure 0
Iof incipient tensile instability, and as such is geometry dependent.
Inspection of the material data in Table I indicates that the
- 0.
1 B
only tensile property which is approximately constant for all 0.GEOMETRY B
three materials is the reduction in area (R.A.).
This suggests that reduction in area might be a good property for correlation 0.60 of the test data.
Before doing so, however, it is convenient to FILLET /
introduce the concept of triaxiality factor (TF) [81.
7z 0.50 -
I
/
STF
= 30"m,,,a/Oreq 0.40 -TFE TER*I" CENTER ET(o
+ 0-2 + 03)
S0.30 a meanRf I BURST PRESSURE 3
0.20I(1 0.10 VI°q 2
+
0.00-L-I 6
=p ca ts 0
4000 8000 12,000 16,000 a-,, a,, o3 principal stresses PRESSURE IPSI)
Note that for uniaxial tension TF = 1, f'or pure'biaxial tension Fig. 5(b)
Stress and strain data for 304 stainless steel disks TF = 2, and for pure triaxial tension TF =
O Transactions of the ASME 4
160 V)
Ln Uj V) 140 120 100 so 60 40 20 0
0.80 0.70 0.60 0.501 0.40
- 0. 30 0:20 0.10 0.00 Fig. 6(a)
Stress and strain data For A-533 B low alloy steel disks z
z 110 140 120 100 6O 60 40 20 0
0.80
- 0. 70 0.60 0.50
- 0. 110
- 0. 30 0.20
- 0. 10 0.00 3
'1000 5000 12..000 16.000 PRI A-533 BPSIk Fig. 6(b)
Stress and strain data for A-533 B low alloy steelI disks Journal of Engineering for Industry z
L.,-
z z
z 120 100 80 66 40 20 0
- 0. 70 0.60 0.50 0.40 0.30
- 0. 20G 0.10 0.00 I
I I
I FILLET GEOMETRY C ENTER I
1/
BURST PRESSURE
,I GEOMETRY C FILLETA
/,/BURST PRESSURE
,IfE INTER!'
I I. -.
4000 8000 12.000 PRESSURE (PSD
- 16. 000 Fig. 6(c)
Stress and strain data for A-533 B low alloy steel disks Fig. 6 Generally, the amount of strain that a material can withstand before fracture is expected to decrease with increasing triaxiality of the imposed stress state. Davis and Connelly [8] have sug gested that the triaxiality factor as defined previously might be an effective parameter with which to study the reduction in ductility due to multiaxial state of stress. That is:
terit
= ecrit Xf(TF) multiaxial uniaxial (2)
Where f(TF) is a monotonically decreasing function.
Investigation of failure data from several sources [9, 10, 11, 12] indicates that, in the absence of severe anisotropy, the follow ing expression is not a bad first approximation of the influence of triaxiality upon ductility:
f(TF) = 1/TF (3)
The triaxiality factors for the disk tests at failure were 2.0 for the centerline region and about 1.65 for the fillet based upon the computed stresses in those regions.
The tensile tests used to measure reduction in area can be assumed to have had a tri axiality factor of 1.0.
In addition, the tensile tests were per formed for both longitudinal and transverse tensile specimens indicating very little anisotropy in the disk materials, so that the approximation of equation [3] should apply.
Thus, as a first approximation of multiaxial ductility, the reduction in area values for the three materials have been divided by the ap propriate triaxiality factors and listed in Table 4.
The final column of Table 4 lists the ratios of equivalent strain in the failure location to the multiaxial ductility at that location.
The correlation is always better than 30 percent, and the average error is about 16 percent.
Casting this same information in a slightly different format, the question of how well the foregoing scheme predicts failure pressure can be answered.
Using the postulate that failure occurs whenever the value of equivalent strain exceeds the re 5
0
- In1 r) 8000
- 2. 000 16 000 1RI.SSURE WSO
160 140 120 100 80 60 40 20 140 120 100 80 60 40 20 0
- 0. 70 0.60 0.50 0.40
- 0. 30 0.20 0.10
- 0. 00 0
4000 8000 12,0330 1.000 PRESSURE (PSI)
Fig. 7(c)
Stress and straiqlata for ABS-C carbon steeldisks Fig. 7 Fig. 7(a)
Stress and strain data for ABS-C carbon steel disks 160 140 120 100 60 40 20 Z
m1 O.,O
- 0. 70 0.60
- 0. 50 0.40 0.30
- 0. 20 0.10 0.00 Fig. 7(b)
Stress and GEOMETRY G BURST PRESSURE 4i0 I
I8 0
0 4000 8'000 1
0
- 12. {000 16 000 r L-SURF. IfSbl strain data for ABS-C carbon steel disks duction in area divided by the triaxiality ratio (multiaxial duc tility) at any point in the disk, burst pressures as well as failure locations can be predicted from the analytical strain versus pres sure curves of Figs. 5, 6, and 7. Table 5 presents such predic tions for the test cases considered here.
The predicted burst pressures give reasonably accurate estimates of the actual burst pressures, and the predicted location of failure was correct in all cases but one (304 S.S.-geometry B).
Summary and Conclusions Results of an elasto-plastic, finite-deformation analysis of selected PVRC disk tests are presented and, in general, there is good agreement between experiment and analysis, which is illustrated by a comparison of the predicted and actual deflec tions at the disk centerline-i as a function of applied pressure.
A definite trend of increasing strain concentration in the fillet of the disks as the strain hardening decreases is apparent in the data for all three geometries analyzed.
The order of magnitude of this trend supports the assumption of Section 3 of the ASME Boiler and Pressure Vessel Code that plastic strain concentration is inversely proportional to the strain hardening exponent, at least for low values of this exponent.
A scheme for predicting burst pressure from the analytical stress and strain data using the reduction in area from a con ventional uniaxial tensile test as a critical strain parameter is suggested.
Failure is posited when the computed equivalent strain in the disks exceeds the reduction in area property of the material adjusted by the triaxiality of the stress state. The scheme is shown to be reasonably consistent for the limited number of cases considered.
This analysis demonstrates that it is possible to predict failure loads for material and hardware similar to those used in commer cial nuclear power plants, provided that a reasonably accurate Transactions of the ASME
(.A (A'
WA z
V)
V)
A z Le W
0 0.80 0.70 0.60 0.50
- 0. 40 0.30 0.20 0.10 0.00 0
PRESSURE (PSI) 6
0.6 GEOMETRY C 0.2 0.4 0.6 0.3 1.0 1.2 1.4 CENTERLINE DEFLECTION (IN)
Strain concentration in fillet for various strain hardening
- 0. 1 "ELASTIC i ftf I I
- ii 0.0 0*.Z
- 0.
0 08 1.0 I?
14 CE,\\[RI.INE DLII FC1 ION INý Fig. 8(b)
Strain concentration in fillet for various strain hardening exponents elasto-plastic analysis can be performed.
Extension of such an analysis to the more complex loading and geometric conditions which exist in actual plant components will allow accurate evaluations of the margins of safety which exist in these com ponents.
0.4
,AZ 0.3
- 0. 2 r-I-
0.1 1-0.0 n : 0.141 n= 0. 242 ELASTIC LINE (n
= I 4
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
.CENTERLINE DEFLECTION (IN)
Fig. 8(c)
Strain concentration in fillet for various strain hardening exponents Fig. 8 Acknowledgments The author would like to thank Mr. G. A. Spiering of Teledyne Materials Research Company for his help in interpreting the test data and Dr. A. L. Thuriman of Westinghouse Bettis Atomic Power Laboratory for the use of his computer program, without which the analysis could not have been performed.
References I Cooper, W. E., Kotteamp, E. H., and Spiering, G. A., "Experi mental Effort on Bursting of Constrained Disks as Related to the Effective Utilization of Yield Strength," ASME, 71-PVP-49, May 1971.
2 P. V. R. C. Subcommittee on Effective Utilization qf Yield Strength Eox*perimental Report of Pilot Program and Phase II Effort on Bursting Constrained Discs, Teledyne Materials Research Co., Technical Report No. E-1 178(b).
3 Thurman, A. L., GAPL-3-A Computer Program for the rn elastic Large Deflection Stravs Analysis of a Thin Plate or Axially Sym metric Shell With Pressure Loading and Deflection Restraints, WAPD TM:-791, Bettis Atomic Power Laboratory, Pittsburgh, Pa., June 1969.
4 Radomski, M., and White, D. J., "Some Theoretical Con siderations Relating to Strain Concentration in Elasto-Plastic Bend ing of Beams," Journal of Strain Analysis, Vol. 3, No. 4, 1968, pp.
- 304-312.
5 4 White, D. J., and [iadomski, M, "Strain Concentration in Beams Under Cyclic Plastic Straining," Journal of Strain Analysis, Vol. 3, No. 4, 1968, pp. 313-324.
Table 4 Computed strains at failure T -
CENTERLNIE DATA EDGE DATA
, RATIOS
'auterial Geocietry Type of i Strain Triaxi
' tty 4iltiavial Strain 7rfioslflitI' j 4ultiaxial iFl1" Fail re lAt Failure FactorlTF)
.I.
(R.A. At Failure Factor (TF) Ductility i'A.
ren
],....
Ductility A ll
.,o 40 2.0
.37
.,1 r.6
.46 1.10 304 S.S Centr 2.0
.37 j
.s5 1.65
.45 1.0 C
Cent-r Z.O
.37.
.41 1
.65
.45 l.s A
Edge
.16 2.0 34
.T2 1.87
.41 1.27 A-5338 a
Edge
.17 2.0
.34
.53 1.67
.41 1.29 C
Cant,,i1 2.0
.34
.38 1.5
.41
-.7, A
Edge
.27 2.0
.33
.52 1.68 1.30 ABE-C 3 Edg
.18 2.0
.33 JO.
1.68
.40 1.20 Edge 1
.33 t t
.40 Solution did not converge at failure ;ressure Journal of Engineering for Industry 0.5 z
-z 0.4
-W 0.3 0.2
- 0. C 0.0 Fig. S(a) exponents Z,
0.6
- 0. 5 0 4i
- 0. 3
- 0. 2 0.6
- 0. 51-1 7
Table 5 Predicted failure data PROICTE) FAIlURR OATA ACTUAh AIURE,MIA Material Geemetry ~Ourst Pressure T
f F "resure iT f
A 12,300 PI Edge 15,000 PSI Edge 3D4 S.S.
8 4,800 PSI Edge 6,500 PSI Cente C
7,400 PSI Center 7,700 PSI Cente A
9,800 PSI Edge 11,000
?St Edge A-533 8 0
,.MDPSI Edge 5,300 PSI Edge C
6,800 PSI Center 6,700 PSI Cente A
8 C
-dge 3
3,150 P'I
""0,4,940 PSI Edqge Edge Edge.........
6 Langer, B. F., "Design-Stress Basis for Pressure Vessels, The William M. Murray Lecture," 1970; Experimental Mechaniav, Jan.
1971. 7 Langer, B. F., "Fatigue Evaluation for Primary-Plus-Second ary Stresses Which Exceed 3S.," Westinghouse Nuclear Energy Systems, June 1969.
8 Davis, E. A., and Connelly, F. M., "Stress Distribution and Plastic Deformation in Rotating Cylinders of Strain-Hardening Material," Journal of Applied Mechanics, TRANS. ASME, Vol. 26, 195-, pp.) ':-o 9 Davis, E. A., "Yielding and Fracture of Medium Carbon Steel Under Combined Stress," Journal of Applied Mechaniav, TRAN3.
ASME, Vol. 67, A-13, Mar. 1945.
10 Siebel, E., and Maier, A., "Dor Einfluss.Melhraclhsiger Span nungszustande auf das Formanderungovermogen Werkstaffe,"
Zietschrift V.D.I., Vol. 77, Dec. 1933.
11 Marin, J., and Hu, L. W., "Plastic Stress Strain Relations for Biaxial Tension and Variable Stress Ratios," Proceedings ofA.S.T.M.,
Vol. 52, 1952.
12 Clausing, D. P., "Effect of Plastic Strain State on Ductility and Toughness," !nternational Journal of Fracture Mechanics, Vol. 6, No. 1, Mar. 1970.
Printed in U. S. A.
Transactions of the ASME a
'ABS-C L
Docket Number 50-346 License Number NPF-3 Serial Number 1-1280 COMMITMENT LIST THE FOLLOWING LIST IDENTIFIES THOSE ACTIONS COMMITTED TO BY THE DAVIS-BESSE NUCLEAR POWER STATION (DBNPS) IN THIS DOCUMENT. ANY OTHER ACTIONS DISCUSSED IN THE SUBMITTAL REPRESENT INTENDED OR PLANNED ACTIONS BY THE DBNPS. THEY ARE DESCRIBED ONLY FOR INFORMATION AND ARE NOT REGULATORY COMMITMENTS. PLEASE NOTIFY THE MANAGER - REGULATORY AFFAIRS (419-321-8450) AT THE DBNPS OF ANY QUESTIONS REGARDING THIS DOCUMENT OR ANY ASSOCIATED REGULATORY COMMITMENTS.
COMMITMENTS DUE DATE None N/A