ML031060646
| ML031060646 | |
| Person / Time | |
|---|---|
| Site: | Point Beach  |
| Issue date: | 02/26/2002 |
| From: | Killian D Framatome ANP |
| To: | Office of Nuclear Reactor Regulation |
| References | |
| 32-5019396-01 | |
| Download: ML031060646 (48) | |
Text
______20697-6 (2/2002)
A .CALCULATION
SUMMARY
SHEET (CSS)
FRAMATOME ANP Document Identifier 32 - 5019396 - 01 Title PB-I CRDM NOZZLE IDTB"'J-GROOVE WELD FLAW EVALUATION PREPARED BY: REVIEWED BY:
METHOD. E DETAILED CHECK 5 INDEPENDENT CALCULATION NAME D.E. KILLIAN NAME H.P. GUNAWARDANE SIGNATURE SIGNATURE I
TITLE ADVISORY ENGR. DATE i/A6z_ TITLE ENGINEER II DATE .9.f- l os COST CENTER 41629 REF.
PAGE(S) 48 TM STATEMENT:
REVIEWER INDEPENDENCE Aii1 PURPOSE AND
SUMMARY
OF RESULTS:
Revision 1: This revision is a non-proprietary version of Revision 0.
The purpose of the present analysis is to assess the suitability of leaving degraded J-groove weld material in the Point Beach Unit 1 reactor vessel head following the repair of a CRDM nozzle by the ID temper bead weld procedure. It is postulated that a small flaw in the head would combine with a large stress corrosion crack in the weld to form a radial comer flaw that would propagate into the low alloy steel head by fatigue crack growth under cyclic loading conditions.
Based on an evaluation of fatigue crack growth into the low alloy steel head and considering the Section Xl requirements of the ASME Code for fracture toughness, a postulated [ ]" radial crack in the Alloy 182 J-groove weld would be acceptable for 25 years of operation.
THE FOLLOWING COMPUTER CODES HAVE BEEN USED IN THIS DOCUMENT: THE DOCUMENT CONTAINS ASSUMPTIONS THAT MUST BE VERIFIED PRIOR TO USE ON SAFETY-RELATED WORK CODE/VERSION/REV CODEIVERSION/REV
_ _YES M NO Page 1 of 48
A FRAMATOME ANP 32-501 9396-01 RECORD OF REVISIONS Affected Revision Pages Description of Revision Date 0 All Original release 9/02 1 All Revision I is a non-proprietary version 2/03 of Revision 0.
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A FRAMATOME ANP 32-5019396-01 CONTENTS Section Heading Paqe 1.0 Introduction ......................... 4 2.0 Geometry and Flaw Model ......................... 6 3.0 Material Properties ......................... 8 4.0 Fracture Mechanics Methodology ........................ 10 5.0 Applied Stresses ........................ 11 6.0 Flaw Evaluations ........................ 18 7.0 Summary of Results ........................ 47 8.0 References ........................ 48 3
A FRAMATOME ANP 32-5019396-01 1.0 Introduction Due to the susceptibility of Alloy 600 partial penetration nozzles to primary water stress corrosion cracking (PWSCC), a repair procedure has been developed for reactor vessel head control rod drive mechanism (CRDM) nozzles at Point Beach Unit 1 (PB-1) wherein the lower portion of a degraded nozzle is removed by a boring procedure and the remaining portion of the nozzle is welded to the low alloy steel reactor vessel head above the original Alloy 182 J-groove attachment weld, as shown in Figure 1. This repair design is more fully described by the design drawing [1]
and the technical requirements document [2]. Except for a chamfer at the comer, the original J-groove weld will not be removed. Since a potential flaw in the J-groove weld can not be sized by currently available non-destructive examination techniques, it must be assumed that the "as-left" condition of the remaining J-groove weld includes degraded or cracked weld material extending through the entire J-groove weld and Alloy 182 butter material. The purpose of the present analysis is to determine from a fracture mechanics viewpoint the suitability of leaving degraded J-groove weld material in the vessel following the repair of a CRDM nozzle.
From analysis of similar CRDM nozzle penetrations in B&W-designed reactor vessel heads [3],
it is known that hoop stresses in the J-groove weld are generally about two times the axial stress at the same location. Since it is expected that this same trend would apply to the PB-I nozzles, the preferential direction for cracking would be axial, or radial relative to the nozzle. It is postulated that a radial crack in the Alloy 182 weld metal would propagate by PWSCC, through the weld and butter, to the interface with the low alloy steel head. It is fully expected that such a crack would then blunt and arrest at the butter-to-head interface [4]. Since the height of the original weld along the bored surface is about 13/4", a radial crack depth extending from the corner of the weld to the low alloy steel head would be very deep. Ductile crack growth through the Alloy 182 material would tend to relieve the residual stresses in the weld as the crack grew to its final size and blunted. Although residual stresses in the head material are low (and even compressive) [7], it is assumed that a small flaw could initiate in the low alloy steel material and grow by fatigue. For the present analysis of the remaining J-groove weld, it is postulated that a small flaw in the head would combine with the stress corrosion crack in the weld to form a large radial comer flaw that would propagate into the low alloy steel head by fatigue crack growth under cyclic loading conditions associated with heatup and cooldown.
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A FRAMATOME ANP 32-5019396-01 Figure 1. ID Temper Bead Weld Repair 5
A FRAMATOME ANP 32-5019396-01 2.0 Geometry and Flaw Model It is postulated that a radial flaw is present in the low alloy steel head, extending from the chamfered corner of the remaining J-groove weld to the interface between the butter and head.
Analytically, this flaw is crudely simulated using the corner flaw model shown below in Figure 2.
I Stress Line Figure 2. Corner Flaw Model The flaw depth, "a", is the radius to the crack front. The stress line shown in the figure above depicts a typical direction for consideration of a one-dimensional variation of stress through the area represented by the corner flaw model.
Since a large flaw would have to be postulated if the J-groove weld was left in its original configuration after removal of the nozzle in the ID temper bead repair procedure, the design drawing 11] specifies a chamfer at the inside corner of the remaining weld to limit the height of the weld along the bored surface, from the inside corner to the low alloy steel head, to [ ]". This configuration was modeled in a three-dimensional finite element structural analysis [6] to determine operating stresses throughout the remaining weld, nozzle, and head. The finite element model of the outermost nozzle location includes a detailed geometrical representation of the remaining J-groove weld prep around the penetration. Stresses are reported along a line originating at the inside comer (Point 0) and oriented about 30° relative to the vertical bored surface on the downhill and uphill sides of the nozzle, as shown in Figure 3. The modeled distance along the line, from Point 0 to the interface between the butter and head, is used to represent the depth of the postulated corner flaw. From Reference 6, the initial flaw depth is a= [ ] in. on the downhill side and a= [ 3 in. on the uphill side 6
A FRAMATOME ANP 32-5019396-01 This figure is not pertinent to th-,yment.
or egibility concerns)
Figure 3. Orientation of Stress Lines 7
A FRAMATOME ANP 32-5019396-01 3.0 Material Properties The portion of the reactor vessel head that contains the CRDM nozzles is fabricated from [
] [2].
Yield Strength From the ASME Code,Section III, Appendix I [8], the specified minimum yield strength for the head material is 50.0 ksi below 100 'F and 43.8 ksi at 600 OF. The value at 600 'F is used as a conservative lower bound for yield strengths at operating temperatures less than 600 OF.
Reference Temperature A reference temperature of 60 'F is used for the RTNDT of the [ ] low alloy reactor vessel head material. This value is commonly used to conservatively represent low alloy ferritic steels.
Fracture Toughness The lower bound Kl, curve of Section Xl, Appendix A, Figure A-4200-1 [9], which can be expressed as Kla = 26.8 + 12.445 exp [ 0.0145 (T - RTNDT) [9 (Article A-4200)]
represents the fracture toughness for crack arrest, where T is the crack tip temperature and RTNDT is the reference nil-ductility temperature of the material. K1, is in ksi'in, and T and RTNDT are in "F. In the present flaw evaluations, KI, is limited to a maximum value of 200 ksilin (upper-shelf fracture toughness). Using the above equation with an RTNDT of 60 OF, Kia equals 200 ksitin at a crack tip temperature of 242 'F.
8
A FRAMATOME ANP 32-5019396-01 Fatigue Crack Growth Flaw growth due to cyclic loading is calculated using the fatigue crack growth rate model from Article A-4300 of Section XI [9],
da =CO (AK, where AK, is the stress intensity factor range in ksi~in and da/dN is in inches/cycle. The crack growth rates for a surface flaw will be used for the evaluation of the corner crack since it is assumed that the degraded condition of the J-groove weld and butter exposes the low alloy steel head material to the primary water environment.
Fatigue Crack Growth Rates for Low Alloy Ferritic Steels in a Primary Water Environment Source: ASME Code, Section Xl, 1998 Edition through 2000 Addenda [9] (Corrected)
AKI = Klmax - Klmin R = Klmin / Klmax 0sRO0.25: AK, <17.74, n = 5.95 C. = 1.02 x 10-1 2 x S S= 1.0 AK , > 17.74, n = 1.95 7
CO = 1.01 x 10 x S S= 1.0 0.25
- R
- 0.65: AK, < 17.74 [ (3.75R + 0.06) / (26.9R -5.725) ]1 25, n = 5.95 CO= 1.02x 10- 12 xS S = 26.9R - 5.725 AK, > 17.74 [(3.75R + 0.06) / (26.9R -5.725) ] 25, n = 1.95 CO= 1.01 x10-7xS S = 3.75R + 0.06 0.65
- R < 1.0: AK, < 12.04, n = 5.95 CO= 1.02 x 10-1 2 x S S= 11.76 AK, > 12.04, n = 1.95 Co= 1.01 x 10-7 xS S = 2.5 9
A FRAMATOME ANP 32-5019396-01 4.0 Fracture Mechanics Methodology The corner crack is analyzed using the following stress intensity factor solution:
K, = Ja{.706(Ao +Ap)+0.537( -Al +0.448 2 A 2 +0.393 - A3]
[ Ref. 10, Eqn. (G-2.2)]
where a is the depth of the crack and Ap is a term added to the Reference 10 solution to account for pressure on the crack face.
The stress distribution in the radial direction is described by the third-order polynomial, C = AO + Aix + A2 x2 + A 3 x3 , [Ref. 10, Eqn. (G-2.1)]
where x is measured from the inside corner.
Irwin Plasticity Correction The Irwin plasticity correction is used to account for a moderate amount of yielding at the crack tip. For plane strain conditions, this correction is defined by
/ 2 r 1y K,(a))
Y 67rt a )
- where, K,(a) = stress intensity factor based on the actual crack length, a, cy = material yield strength.
A stress intensity factor, K,(ae ), is then calculated based on the effective crack length, ae = a + ry.
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A FRAMATOME ANP 32-5019396-01 5.0 Applied Stresses Operational stresses are obtained from the results of a three-dimensional linear finite element analysis of the outermost CRDM nozzle head penetration that addresses the configuration after repair by the ID temper bead weld procedure of Reference 1. Stresses are available from Reference 6 at the 0° (downhill) and 1800 (uphill) sides of the nozzle bore for seven transients:
plant heatup and cooldown, plant loading and unloading, 10% step load increase and decrease, 50% step load reduction, reactor trip, loss of flow, and loss of load. Stresses were reported in a cylindrical coordinate system relative to the nozzle so that the stress directions remain constant around the nozzle. For the most part, the largest hoop stresses at the crack tip are at the downhill side of the nozzle bore (0° location). These stresses are perpendicular to the crack face and tend to open the corner crack. The operational stresses from Reference 6, calculated for the outermost CRDM nozzle location, conservatively bound the stresses at all other nozzle locations.
Table I presents the maximum and minimum hoop stresses for each transient. Due to the dominating influence of pressure on stress, stresses remain positive for all transient conditions.
Stresses are listed in Table 1 for the downhill (0°) location as a function of the radial position along the stress line shown in Figures 2 and 3. Nine positions are used to report stresses along the stress line: the first 4 positions are within the weld material, the fifth position is at the butter/head interface, and the last 4 positions are located in the reactor vessel head base metal.
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A PPAMAATn~MF AMP 32-5019396-01 Table 1. Operational Hoop Stresses on Downhill Side (6]
Parameter Loading Condition Transient Heatup/Cooldown Plant Loading/Unloading 10% Load Changes 50% Load Reduction Time 0.001 hr. 6.0 hr. 0.333 hr. 3.333 hr. 0.0625 hr. 1.025 hr. 0.05 hr. 0.233 hr.
Temperature 100 OF 540 OF 612 OF 547 OF 587 OF 602 OF 590 OF 548 OF Pressure I psig [ ]psig [ ]psig [ ] psig [ Ipsig [ ] psig [ ] psig [ ] psig x (in.)* SY (psi) SY (psi) SY (psi) SY (psi) SY (psi) SY (psi) SY (psi) SY (psi) 0.0000 [ ] [ ] [ ] [ ] [ ] [ I [ ] [ ]
0.2022 [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
0.4043 [ ] [ ] [ ] [ ] [ ] [ ] [ ] [
0.6065 l ] [ ] [ ] [ ] [ ] [ ] [ ] [
0.8087 0.8087 [ ] [ ] [ ] [ ] [ ] [ ] [ ] [I 1.1043 [ ] [ ] [ ] [ ] [ ] [ ] [ ] ]
1.39 1.3999 [ ] [ ] [ ] ] [ ] [ ] [ ] [ ]
1.6955 [ ] [ ] [ ] [ ] [ ] [ ] [ ] [
1.9911 [ 1 [ 1 [ 1 [ ] [ ] [ ] [ ] [ ]
- Cumulative distance along path line PW_0 in Reference 6.
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A FRAMATOME ANP 32-5019396-01 Table 1. Operational Hoop Stresses on Downhill Side [6] (Cont'd)
Parameter Loading Condition Transient Reactor Trip Loss of Flow Loss of Load Time 0.0167 hr. 0.025 hr. 0.001 hr. 0.0403 hr. 0.00278 hr. 0.0444 hr.
Temperature 550 OF 547 OF 612 OF 528 OF 655 OF 550 °F Pressure ]psig [ ]psig [ ]Psig ]psig [ ]psig ] psig x (in.) SY (psi) SY (psi) SY (psi) SY (psi) SY (psi) SY (psi) 0.0000 [ ] [ ] [ ] [ ] [ I [
0.2022 [ ] [ ] [ ] [ ] [ ] [ ]
0.4043 [ ] ] [ ] [ ] [ ] [ ]
0.6065 [ ] [ ] [ ] ] [ ] [
0.8087 [ [ ] [ ] [ ] [ ] [ ]
1.1043 ] [ ] [ ] [ ] [ ] [ ]
1.3999[ 3 [ ][ ][ ][ ][ ]
1.6955[ ] [ ] [ ][ ][ ][ ]
1.991 1[ ] [ ][ ][ ][ ][ ]
- Cumulative distance along path line PW_0 in Reference 6.
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A 32-5019396-01 FRAMATOME ANP Residual stresses are not considered in the present flaw evaluations since a crack that has propagated all the way through the weld and butter would tend to relieve these stresses. A three-dimensional elastic-plastic finite element analysis was performed by Dominion Engineering, Inc. [7] to simulate the sequence of steps involved in arriving at the configuration of the CRDM nozzle and RV head after completion of the ID temper bead repair. This analysis simulated the heatup of the weld, butter, and adjacent material during the welding process and the subsequent cooldown to ambient temperature, a pre-service hydro test, and operation at steady state conditions. After the steady state loads were removed, and the structure was again at ambient conditions, the lower portion of the nozzle was deleted from the model, the new ID temper bead repair weld was added using an 8-pass weld simulation, and the J-groove weld was chamfered by removing selected elements. The stresses associated with this repair configuration are the residual stresses corresponding to an unflawed structure.
The residual stresses from the Dominion Engineering analysis are listed in Table 2 and plotted in Figure 5. These stresses are in the original weld, after chamfering. Although the residual hoop stress in the weld region is high, up to about [ ] psi, the stress decreases to zero within the butter region and is compressive in the head. These stresses would be relieved as the crack propagates through the weld, so that only the operating stresses from Table 1 need be considered when evaluating a crack at the butter-to-head interface.
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Framatome ANP 32-5019396-01 Table 2.
Residual Hoop Stresses in the Unflawed Structure After Nozzle Removal, 8-Pass Weld Simulation, and Chamfer [7]
ANSYS Load Step: 20011 Global Coordinates Hoop Node X Z AS(') Location Stress (in.) (in.) (in.) (psi) 1309 2.0000 66.802 0.000 Inside Surface of Weld 1412 2.1810 66.961 0.241 Weld 1615 2.3895 67.162 0.530 Weld/Butter Interface 1818 2.6315 67.425 0.887 Butter/Head Interface 1918 2.6694 67.648 1.113 Head 2018 2.7072 67.871 1.339 Head 2118 2.7451 68.093 1.565 Head 2218 2.7830 68.316 1.791 Head 2318 2.8209 68.539 2.017 Head 2418 2.8587 68.762 2.243 Head 2518 2.9163 69.100 2.586 Head 2618 2.9815 69.484 2.976 Head 2718 3.0556 69.920 3.418 Head
{ Distance along a stress line, originating at the inside corner of the chamfered weld, and passing through the "outside corner" of the J-groove weld prep (see Figure 4).
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A FRAMATOME ANP 32-501 9396-01 Stress Line for t Residual Stresses Figure 4. Weld Geometry After Chamfer 16
Framatome ANP 32-501 9396-01 Figure 5. Residual Hoop Stresses After Weld Repair
._n 0-U) a 0
0 a:
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Distance from Surface, in.
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A FRAMATOME ANP 32-501 9396-01 6.0 Flaw Evaluations A fracture mechanics analysis is performed considering fatigue crack growth over 25 years of service to determine a final flaw size for calculating stress intensity factors for comparison with the fracture toughness requirements of Section Xl. Article IWB-3612 [10] requires that a safety factor of 410 be used when comparing the applied stress intensity factor to the material fracture toughness. Calculations are performed for a postulated radial corner crack on the downhill side of the outermost CRDM nozzle head penetration.
The actual fracture mechanics calculations are presented in Tables 3 through 9 for the seven transients considered in the finite element stress analysis [6]. Operational hoop stresses perpendicular to the plane of the postulated crack are obtained from Table 1. Fatigue crack growth is calculated on a yearly basis using the following pattern for accumulating cycles:
Table Transient Cycles / 40 Years Cycles / Year 3 Heatup and Cooldown 200 5 4 Plant Loading and Unloading 3,000 75 5 10% Step Load Changes 2,000 50 6 50% Step Load Reduction 200 5 7 Reactor Trip 400 10 8 Loss of Flow 80 2 9 Loss of Load 80 2 These cycles are distributed uniformly over the 25 year service life by linking the incremental crack growth between Tables 3 through 9.
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Frarnatome ANP 32-501 9396-01 Table 3. Evaluation of CRDM Nozzle Corner Crack for Heatup/Cooldown INPUT DATA Initial Flaw Size: Depth, j in.
Material Data: Yield strength, SY = 43.8 ksi Reference temp., RTndt = 60 F Upper shelf tough. = 200 ksilin Kla = 26.8 + 12.445 exp [ 0.0145 (T - RTndt) ]
Kla is limited to the upper shelf toughness.
Applied Loads:
Loading Conditions Ss* HU**
Temperature (F) 540 100 Pressure (ksi)
Kla (ksiin)
Position 200 49 x Hoop Stress (in.) (ksi) (ksi) 0.0000 0.2022 0.4043 0.6065 0.8087 1.1043 1.3999 1.6955 1.9911
- Heatup/Cooldown Transient at 6.0 hours0 days <br />0 hours <br />0 weeks <br />0 months <br /> (steady state)
- Heatup/Cooldown Transient at 0.001 hours1.157407e-5 days <br />2.777778e-4 hours <br />1.653439e-6 weeks <br />3.805e-7 months <br /> (low temperature)
PB-I CRDM HU-CD NP.xls 19
Framatome ANP 32-501 9396-01 Table 3. Evaluation of CRDM Nozzle Corner Crack for Heatup/Cooldown (Cont'd)
STRESS INTENSITY FACTOR Kl(a) = 4(7a) [ 0.706(A0 +Ap) + 0.537(2aht)A 1 + 0.448(a2 /2)A2 + 0.393(4a 3 /3n)A 3 ]
where the through-wall stress distribution is described by the third order polynomial, S(x) = Ao + A1x + A 2X? + A3x3 ,
defined by:
Stress Loading Conditions Coeff. SS HU (ksi) (ksi)
Ao Al A2 A3 Effective crack size:
a, = a + 1I(67r)N[Kl(a)/Sy] 2 Effective stress intensity factor:
KI(ae) = A(nae) [ 0.706(AO+Ap) + 0.537(2ae/h)A, + 0.448(ae 12)A2 + 0.393(4ae3 /3tt)A 3 ]
PB-1 CRDM HU-CD NP.xls 20
Framatome ANP 32-5019396-01 Table 3. Evaluation of CRDM Nozzle Corner Crack for Heatup/Cooldown (Cont'd)
FATIGUE CRACK GROWTH Transient
Description:
200 cycles over 40 years AN = 5 cycles/year Operating Ss HU Ss HU Ss HU SS HU Time Cycle a Kl(a) KI(a) AKI Aa ae an Kl(ae) KI(ae) Margin = Kla / KI(ae)
(yr.) (in.) (ksiqin) (ksiqin) (ksliin) (in.) (in.) (in..) (ksiqin) (ksiqin)
I ,-
0 0 41.63 7.34 34.28 0.00050 42.58 7.35 4.70 6.67 1 5 41.77 7.37 34.40 0.00050 42.72 7.37 4.68 6.65 2 10 41.91 7.39 34.52 0.00050 42.86 7.40 4.67 6.63 3 15 42.05 7.42 34.64 0.00051 43.00 7.42 4.65 6.60 4 20 42.20 7.44 34.75 0.00051 43.14 7.45 4.64 6.58 5 25 42.34 7.47 34.87 0.00051 43.27 7.47 4.62 6.56 6 30 42.48 7.49 34.98 0.00052 43.41 7.50 4.61 6.54 7 35 42.61 7.52 35.10 0.00052 43.55 7.52 4.59 6.52 8 40 42.75 7.54 35.21 0.00052 43.68 7.55 4.58 6.50 9 45 42.89 7.56 35.33 0.00053 43.82 7.57 4.56 6.48 10 50 43.03 7.59 35.44 0.00053 43.95 7.59 4.55 6.46 11 55 43.16 7.61 35.55 0.00053 44.09 7.62 4.54 6.44 12 60 43.30 7.64 35.66 0.00054 44.22 7.64 4.52 6.42 13 65 43.43 7.66 35.77 0.00054 44.35 7.67 4.51 6.40 14 70 43.57 7.68 35.88 0.00054 44.49 7.69 4.50 6.38 15 75 43.70 7.71 35.99 0.00055 44.62 7.71 4.48 6.36 16 80 43.83 7.73 36.10 0.00055 44.75 7.74 4.47 6.34 17 85 43.97 7.75 36.21 0.00055 44.88 7.76 4.46 6.32 18 90 44.10 7.78 36.32 0.00056 45.00 7.78 4.44 6.30 19 95 44.23 7.80 36.43 0.00056 45.13 7.81 4.43 6.28 20 100 44.36 7.82 36.54 0.00056 45.26 7.83 4.42 6.26 21 105 44.49 7.85 36.64 0.00057 45.38 7.85 4.41 6.24 22 110 44.62 7.87 36.75 0.00057 45.51 7.87 4.39 6.23 23 115 44.74 7.89 36.85 0.00057 45.63 7.90 4.38 6.21 24 120 44.87 7.91 36.96 0.00058 45.76 7.92 4.37 6.19 25 125 45.00 7.94 37.06 0.00058 45.88 7.94 4.36 6.17 PB-1 CRDM HU-CD NP.xls 21
Framatome ANP 32-501 9396-01 Table 3. Evaluation of CRDM Nozzle Corner Crack for Heatup/Cooldown (Cont'd)
FRACTURE TOUGHNESS MARGINS Period of Operation: Time = 25.00 years Final Flaw Size: a= E ] in. (after loss of load transient)
Margin = Kla / KI(ae)
Loading Conditions SS HU Fracture Toughness, Kla 200 49 ksi'ln KI(a) 45.12 7.96 ksilmn ae Kl(aj) 46.00 7.96 ksiin Actual Margin 4.35 6.16 Required Margin 3.16 3.16 PB-i CRDM HU-CD NP.xls 22
Framatome ANP 32-5019396-01 Table 4. Evaluation of CRDM Nozzle Corner Crack for Plant Loading/Unloading INPUT DATA Initial Flaw Size: Depth, a= ]j in.
Material Data: Yield strength, Sy= 43.8 ksi Reference temp., RTndt = 60 F Upper shelf tough. = 200 ksi'lin Kla = 26.8 + 12.445 exp [ 0.0145 (T - RTndt) ]
Kla is limited to the upper shelf toughness.
Applied Loads:
Loading Conditions PU* PL**
Temperature (F) 547 612 Pressure, p (ksi)
Kla (ksi~in)
Position 200 200 x Hoop Stress (in.) (ksi) (ksi) 0.0000 0.2022 0.4043 0.6065 0.8087 1.1043 1.3999 1.6955 1.9911
- Plant Loading/Unloading Transient at 3.333 hours0.00385 days <br />0.0925 hours <br />5.505952e-4 weeks <br />1.267065e-4 months <br /> (plant unloading)
- Plant Loading/Unloading Transient at 0.333 hours0.00385 days <br />0.0925 hours <br />5.505952e-4 weeks <br />1.267065e-4 months <br /> (plant loading)
PB-1 CRDM Load-Unload NP.xls 23
Framatome ANP 32-501 9396-01 Table 4. Evaluation of CRDM Nozzle Corner Crack for Plant Loading/Unloading (Cont'd)
STRESS INTENSITY FACTOR 2 3 KI(a) = 4(na) [ 0.706(AO+Ap) + 0.537(2afiT)A 1 + 0.448(a /2)A2 + 0.393(4a /37)A 3]
where the through-wall stress distribution is described by the third order polynomial, S(x) = Ao + A1 x + A2x2 + A3 x3 ,
defined by:
Stress Loading Conditions Coeff. PU PL (ksi) (ksi)
Ao Al A2 A3 Effective crack size:
ae = a + 1/(67Tr)*[KI(a)pSyf 2 Effective stress intensity factor:
3 KI(ae) = (7Tae) [ 0.706(AO+Ap) + 0.537(2aeht)AI + 0.448(ae2 /2)A2 + 0.393(4ae /3Tc)A3 ]
PB-1 CRDM Load-Unload NP.xls 24
Framatome ANP 32-501 9396-01 Table 4. Evaluation of CRDM Nozzle Corner Crack for Plant Loading/Unloading (Cont'd)
FATIGUE CRACK GROWTH Transient
Description:
3000 cycles over 40 years AN = 75 cycles/year Operating PU PL PU PL PU PL PU PL Time Cycle a Kl(a) Kl(a) AKI Aa a6 a, KI(a,) KI(ae) Margin = Kla / Kl(a.)
_(yr.) (in.) (ksiNIin) (ksi~in) (ksiqlin) (in.) (in.) (in.) (ksinJin) (ksiqin) 0 0 49.86 28.92 20.94 0.00638 51.25 29.30 3.90 6.83 1 75 50.01 29.03 20.97 0.00640 51.39 29.41 3.89 6.80 2 150 50.15 29.15 21.00 0.00643 51.53 29.53 3.88 6.77 3 225 50.30 29.27 21.04 0.00645 51.67 29.65 3.87 6.75 4 300 50.45 29.38 21.07 0.00648 51.81 29.76 3.86 6.72 5 375 50.59 29.50 21.10 0.00650 51.94 29.88 3.85 6.69 6 450 50.74 29.61 21.13 0.00653 52.08 29.99 3.84 6.67 7 525 50.88 29.73 21.16 0.00655 52.21 30.11 3.83 6.64 8 600 51.02 29.84 21.18 0.00657 52.35 30.22 3.82 6.62 9 675 51.16 29.95 21.21 0.00660 52.48 30.33 3.81 6.59 10 750 51.30 30.07 21.24 0.00662 52.61 30.45 3.80 6.57 11 825 51.44 30.18 21.26 0.00664 52.74 30.56 3.79 6.54 12 900 51.58 30.29 21.29 0.00667 52.87 30.67 3.78 6.52 13 975 51.72 30.40 21.31 0.00669 53.00 30.78 3.77 6.50 14 1050 51.85 30.51 21.34 0.00671 53.12 30.89 3.76 6.47 15 1125 51.99 30.63 21.36 0.00673 53.25 31.01 3.76 6.45 16 1200 52.12 30.74 21.38 0.00675 53.37 31.12 3.75 6.43 17 1275 52.25 30.85 21.41 0.00677 53.49 31.23 3.74 6.40 18 1350 52.38 30.96 21.43 0.00679 53.61 31.34 3.73 6.38 19 1425 52.51 31.06 21.45 0.00681 53.73 31.44 3.72 6.36 20 1500 52.64 31.17 21.47 0.00683 53.85 31.55 3.71 6.34 21 1575 52.77 31.28 21.49 0.00685 53.97 31.66 3.71 6.32 22 1650 52.89 31.39 21.50 0.00687 54.09 31.77 3.70 6.30 23 1725 53.02 31.50 21.52 0.00688 54.20 31.87 3.69 6.27 24 1800 53.14 31.60 21.54 0.00690 54.31 31.98 3.68 6.25 25 1875 53.26 31.71 21.55 0.00692 54.43 32.09 3.67 6.23 PB-1 CROM Load-Unload NP.xls 25
Framatome ANP 32-501 9396-01 Table 4. Evaluation of CRDM Nozzle Corner Crack for Plant Loading/Unloading (Cont'd)
FRACTURE TOUGHNESS MARGINS Period of Operation: Time = 25.00 years Final Flaw Size: a= [ ] in. (after loss of load transient)
Margin = Kla I KI(ae)
Loading Conditions PU PL Fracture Toughness, Kla 200.0 200.0 ksivin KI(a) 53.37 31.81 ksi4in a,
Kl(ae) 54.53 32.18 ksiiin Actual Margin 3.67 6.21 Required Margin 3.16 3.16 PB-i CRDM Load-Unload NP.xIs 26
Framatome ANP 32^501 9396-01 Table 5. Evaluation of CRDM Nozzle Corner Crack for 10% Step Load Changes INPUT DATA Initial Flaw Size: Depth, a= [ ] in.
Material Data: Yield strength, Sy = 43.8 ksi Reference temp., RTndt = 60 F Upper shelf tough. = 200 ksiqin Kla = 26.8 + 12.445 exp [0.0145 (T - RTndt) ]
Kla is limited to the upper shelf toughness.
Applied Loads:
Loading Conditions IOSI* 1OSD^*
Temperature (F) 587 602 Pressure, p (ksi)
KKla (ksiqin)
Position 200 200 x Hoop Stress (in.) (ksi) (ksi) 0.0000 0.2022 0.4043 0.6065 0.8087 1.1043 1.3999 1.6955 1.9911
- 10% Step Load Change at 0.0625 hours0.00723 days <br />0.174 hours <br />0.00103 weeks <br />2.378125e-4 months <br /> (step increase)
- 10% Step Load Change at 1.025 hours2.893519e-4 days <br />0.00694 hours <br />4.133598e-5 weeks <br />9.5125e-6 months <br /> (step decrease)
PB-1 CRDM 10% Step Load NP.xis 27
Framatome ANP 32-501 9396-01 Table 5. Evaluation of CRDM Nozzle Corner Crack for 10% Step Load Changes (Cont'd)
STRESS INTENSITY FACTOR Kl(a) = ¶I(Ita) [ 0.706(AO+Ap) + 0.537(2a/it)A 1 + 0.448(a 2 /2)A 2 + 0.393(4a3 /3ir)A3 ]
where the through-wall stress distribution is described by the third order polynomial, S(x) = AO + Aix + A2x2 + A3x3.
defined by:
Stress Loading Conditions Coeff. 1OSI 10SD (ksi) (ksi)
Ao Al A2 A3 Effective crack size:
ae = a + 1/(67t)*[KI(a)/Sy]2 Effective stress intensity factor:
Kl(ae) = (Niae) [ 0.706(Ao+Ap) + 0.537(2aeht)AI + 0.448(ae 2 /2)A, + 0.393(4ae 3 /3n)A3 ]
PB-1 CRDM 10% Step Load NP.xls 28
Framatome ANP 32-6019396-01 Table 5. Evaluation of CRDM Nozzle Corner Crack for 10% Step Load Changes (Cont'd)
FATIGUE CRACK GROWTH Transient
Description:
2000 cycles over 40 years AN = 50 cycles/year Operating 10SI 1OSD 10SI 1OSD 10SI 1OSD 10SI 1OSD Time Cycle a Kl(a) Kl(a) AKI Aa ae a, KI(ae) KI(ae) Margin = Kla I Ki(ae)
(yr.) (in.) (ksiqin) (ksiqin) (ksiqin) (in.) (in.) (in.) (ksiqin) (ksiqin) 0 41.82 38.45 3.37 0.00000 42.73 39.20 4.68 5.10 1 50 41.96 38.58 3.38 0.00000 42.87 39.34 4.67 5.08 2 100 42.09 38.71 3.38 0.00000 43.00 39.47 4.65 5.07 3 150 42.23 38.85 3.38 0.00000 43.13 39.60 4.64 5.05 4 200 42.36 38.98 3.39 0.00000 43.27 39.73 4.62 5.03 5 250 42.50 39.11 3.39 0.00000 43.40 39.86 4.61 5.02 6 300 42.63 39.24 3.39 0.00000 43.53 39.98 4.59 5.00 7 350 42.77 39.37 3.40 0.00000 43.66 40.11 4.58 4.99 8 400 42.90 39.50 3.40 0.00000 43.78 40.24 4.57 4.97 9 450 43.03 39.63 3.40 0.00000 43.91 40.36 4.55 4.95 10 500 43.16 39.75 3.40 0.00000 44.04 40.49 4.54 4.94 11 550 43.29 39.88 3.41 0.00000 44.16 40.61 4.53 4.92 12 600 43.42 40.01 3.41 0.00000 44.29 40.74 4.52 4.91 13 650 43.54 40.13 3.41 0.00000 44.41 40.86 4.50 4.89 14 700 43.67 40.26 3.41 0.00000 44.53 40.98 4.49 4.88 15 750 43.80 40.38 3.42 0.00000 44.65 41.10 4.48 4.87 16 800 43.92 40.50 3.42 0.00000 44.77 41.22 4.47 4.85 17 850 44.05 40.62 3.42 0.00000 44.89 41.34 4.45 4.84 18 900 44.17 40.75 3.42 0.00000 45.01 41.46 4.44 4.82 19 950 44.29 40.87 3.42 0.00000 45.13 41.58 4.43 4.81 20 1000 44.41 40.99 3.43 0.00000 45.25 41.69 4.42 4.80 21 1050 44.53 41.10 3.43 0.00000 45.36 41.81 4.41 4.78 22 1100 44.65 41.22 3.43 0.00000 45.48 41.92 4.40 4.77 23 1150 44.77 41.34 3.43 0.00000 45.59 42.04 4.39 4.76 24 1200 44.89 41.46 3.43 0.00000 45.70 42.15 4.38 4.75 25 1250 45.00 41.57 3.43 0.00000 45.81 42.26 4.37 4.73 PB-1 CRDM 10% Step Load NP.xls 29
Framatome ANP 32-5019396-01 Table 5. Evaluation of CRDM Nozzle Corner Crack for 10% Step Load Changes (Cont'd)
FRACTURE TOUGHNESS MARGINS Period of Operation: Time = 25.00 years Final Flaw Size: a= [ ] in. (after loss of load transient)
Margin = Kla / KI(ae)
Loading Conditions 10SI 1OSD Fracture Toughness, Kla 200.0 200.0 ksiJin Kl(a) 45.01 41.57 ksivin ae Kl(aj) 45.82 42.26 ksi'Jin Actual Margin 4.37 4.73 Required Margin 3.16 3.16 PB-i CRDM 10% Step Load NP.xls 30
Framatome ANP 32-501 9396-01 Table 6. Evaluation of CRDM Nozzle Corner Crack for 50% Step Load Reduction INPUT DATA Initial Flaw Size: Depth, a =E j2in.
Material Data: Yield strength, Sy = 43.8 ksi Reference temp., RTndt= 60 F Upper shelf tough. = 200 ksiIin Kla = 26.8 + 12.445 exp [ 0.0145 (T - RTndt) ]
Kla is limited to the upper shelf toughness.
Applied Loads:
Loading Conditions 50SR1* 50SR2**
Temperature (F) 548 590 Pressure, p (ksi)
Kla (ksiin)
Position 200 200 x Hoop Stress (in.) (ksi) (ksi) 0.0000 0.2022 0.4043 0.6065 0.8087 1.1043 1.3999 1.6955 1.9911
- 50% Step Load Reduction at 0.233 hours0.0027 days <br />0.0647 hours <br />3.852513e-4 weeks <br />8.86565e-5 months <br /> (max. stress)
- 50% Step Load Reduction at 0.05 hours5.787037e-5 days <br />0.00139 hours <br />8.267196e-6 weeks <br />1.9025e-6 months <br /> (min. stress)
PB-1 CRDM 50% Step Load NP.xls 31
Framatome ANP 32-501 9396-01 Table 6. Evaluation of CRDM Nozzle Corner Crack for 50% Step Load Reduction (Cont'd)
STRESS INTENSITY FACTOR KI(a) = l(7ra) [ 0.706(AO+Ap) + 0.537(2a/h)A 1 + 0.448(a 2 /2)A 2 + 0.393(4a3 /3it)A3 ]
where the through-wall stress distribution is described by the third order polynomial,
+ A2x2 + A 3x ,
3 S(x) = AO + Ajx defined by:
Stress Loading Conditions Coeff. 50SR1 50SR2 (ksi) (ksi)
Ao A1 A2 A3 Effective crack size:
ae = a + 1/(6nr)*[KI(a)/SY12 Effective stress intensity factor:
3 KI(ae) = 4(nae) [ 0.706(AO+Ap) + 0.537(2ae,/)AI + 0.448(ae 2 /2)A2 + 0.393(4a 8 /37)A 3 ]
PB-I CRDM 50% Step Load NP.xls 32
Framatome ANP 32-501 9396-01 Table 6. Evaluation of CRDM Nozzle Corner Crack for 50% Step Load Reduction (Cont'd)
FATIGUE CRACK GROWTH Transient
Description:
200 cycles over 40 years AN = 5 cycles/year Operating 50SR1 50SR2 50SRI 50SR2 50SR1 50SR2 50SR1 50SR2 Time Cycle a Kl(a) KI(a) AKI Aa ae a, KI(ae) Kl(ae) Margin = Kla / KI(a,)
(yr.) (in.) (ksi~in) (ksiqlin) (ksi4in) (in.) (in.) (in.) (ksiqin) (ksi'lin) 39.74 4.54 5.03 0 0 43.12 38.95 4.17 0.00000 44.07 5 43.25 39.09 4.17 0.00000 44.20 39.88 4.52 5.02 2 10 43.39 39.22 4.17 0.00000 44.33 40.01 4.51 5.00 3 15 43.52 39.36 4.16 0.00000 44.46 40.14 4.50 4.98 4 20 43.66 39.49 4.16 0.00000 44.59 40.28 4.49 4.97 5 25 43.79 39.63 4.16 0.00000 44.72 40.41 4.47 4.95 6 30 43.92 39.76 4.16 0.00000 44.85 40.54 4.46 4.93 7 35 44.05 39.89 4.16 0.00000 44.97 40.67 4.45 4.92 8 40 44.18 40.02 4.16 0.00000 45.10 40.80 4.43 4.90 9 45 44.31 40.15 4.15 0.00000 45.22 40.92 4.42 4.89 10 50 44.43 40.28 4.15 0.00000 45.34 41.05 4.41 4.87 11 55 44.56 40.41 4.15 0.00000 45.47 41.18 4.40 4.86 12 60 44.69 40.54 4.15 0.00000 45.59 41.30 4.39 4.84 13 65 44.81 40.67 4.14 0.00000 45.71 41.43 4.38 4.83 14 70 44.94 40.80 4.14 0.00000 45.83 41.55 4.36 4.81 15 75 45.06 40.92 4.14 0.00000 45.95 41.68 4.35 4.80 16 80 45.18 41.05 4.14 0.00000 46.06 41.80 4.34 4.78 17 85 45.30 41.17 4.13 0.00000 46.18 41.92 4.33 4.77 18 90 45.42 41.30 4.13 0.00000 46.30 42.04 4.32 4.76 19 95 45.54 41.42 4.13 0.00000 46.41 42.16 4.31 4.74 20 100 45.66 41.54 4.12 0.00000 46.52 42.28 4.30 4.73 21 105 45.78 41.66 4.12 0.00000 46.64 42.40 4.29 4.72 22 110 45.90 41.78 4.11 0.00000 46.75 42.52 4.28 4.70 23 115 46.01 41.90 4.11 0.00000 46.86 42.64 4.27 4.69 24 120 46.13 42.02 4.11 0.00000 46.97 42.75 4.26 4.68 25 125 46.24 42.14 4.10 0.00000 47.08 42.87 4.25 4.67 PB-1 CRDM 50% Step Load NP.xls 33
Framatome ANP 32-5019396-01 Table 6. Evaluation of CRDM Nozzle Corner Crack for 50% Step Load Reduction (Cont'd)
FRACTURE TOUGHNESS MARGINS Period of Operation: Time = 25.00 years Final Flaw Size: a= [ ] in. (after loss of load transient)
Margin = Kla / KI(ae)
Loading Conditions 50SR1 50SR2 Fracture Toughness, Kla 200.0 200.0 ksiIin KI(a) 46.24 42.14 ksi-4in a.
Kl(a.) 47.08 42.87 ksi4in Actual Margin 4.25 4.67 Required Margin 3.16 3.16 PB-i CRDM 50% Step Load NP.xIs 34
Framatome ANP 32-501 9396-01 Table 7. Evaluation of CRDM Nozzle Corner Crack for Reactor Trip INPUT DATA Initial Flaw Size: Depth, a=CE ]in.
Material Data: Yield strength, Sy = 43.8 ksi Reference temp., RTndt = 60 F Upper shelf tough. = 200 ksWin Kla = 26.8 + 12.445 exp [0.0145 (T - RTndt) ]
Kla is limited to the upper shelf toughness.
Applied Loads:
Loading Conditions RT1
- RT2**
Temperature (F) 547 550 Pressure, p (ksi)
Kla (ks Win Position i 200 200 x Hoop Stress (in.) (ksi) (ksi) 0.0000 0.2022 0.4043 0.6065 0.8087 1.1043 1.3999 1.6955 1.9911
- Reactor Trip Transient at 0.025 hours2.893519e-4 days <br />0.00694 hours <br />4.133598e-5 weeks <br />9.5125e-6 months <br /> (max. stress) i* Reactor Trip Transient at 0.0167 hours0.00193 days <br />0.0464 hours <br />2.761243e-4 weeks <br />6.35435e-5 months <br /> (min. stress)
PB-i CRDM Reactor Trip NP.xls 35
Framatome ANP 32-501 9396-01 Table 7. Evaluation of CRDM Nozzle Corner Crack for Reactor Trip (Cont'd)
STRESS INTENSITY FACTOR Kl(a) = 4(na) [ 0.706(AO+Ap) + 0.537(2a/Tc)A 1 + 0.448(a2 /2)A 2 + 0.393(4a3 13n)A 3 ]
where the through-wall stress distribution is described by the third order polynomial, S(x) = Ao + Aix + A2 x2 + A3x3, defined by:
Stress Loading Conditions Coeff. RT1 RT2 (ksi) (ksi)
Ao A,
A2 A3 Effective crack size:
ae = a + 1/(6t)*[Kl(a)/Sy]2 Effective stress intensity factor Kl(ae) = 4(7rae) [ 0.706(A,+Ap) + 0.537(2aeht)A, + 0.448(ae 2/2)A2 + 0.393(4ae 3i3n)A3 ]
PB-i CRDM Reactor Trip NP.xls 36
Framatome ANP 32-501 9396-01 Table 7. Evaluation of CRDM Nozzle Corner Crack for Reactor Trip (Cont'd)
FATIGUE CRACK GROWTH Transient
Description:
400 cycles over 40 years AN = 10 cycles/year Operating RT1 RT2 RT1 RT2 RT1 RT2 RT1 RT2 Time Cycle a Kl(a) Kl(a) AKI ha ae a, KI(ae) Kl(ae) Margin = Kla / Kl(ae)
(yr.) (in.) (ksi4in) (ksilin) (ksiqin) (in.) (in.) (in.) (ksNin) (ksilin) .
47.21 44.42 4.24 4.50 0 0 46.23 43.60 2.63 0.00000 1 10 46.36 43.71 2.64 0.00000 47.32 44.53 4.23 4.49 2 20 46.48 43.83 2.65 0.00000 47.44 44.64 4.22 4.48 3 30 46.60 43.94 2.65 0.00000 47.55 44.75 4.21 4.47 4 40 46.72 44.06 2.66 0.00000 47.66 44.85 4.20 4.46 5 50 46.84 44.17 2.67 0.00000 47.77 44.96 4.19 4.45 6 60 46.95 44.28 2.67 0.00000 47.88 45.06 4.18 4.44 7 70 47.07 44.39 2.68 0.00000 47.99 45.17 4.17 4.43 8 80 47.18 44.50 2.69 0.00000 48.09 45.27 4.16 4.42 9 90 47.30 44.60 2.69 0.00000 48.20 45.37 4.15 4.41 10 100 47.41 44.71 2.70 0.00000 48.30 45.47 4.14 4.40 11 110 47.52 44.82 2.70 0.00000 48.40 45.57 4.13 4.39 12 120 47.63 44.92 2.71 0.00000 48.50 45.66 4.12 4.38 13 130 47.74 45.02 2.72 0.00000 48.60 45.76 4.11 4.37 14 140 47.85 45.13 2.72 0.00000 48.70 45.85 4.11 4.36 15 150 47.95 45.23 2.73 0.00000 48.80 45.95 4.10 4.35 16 160 48.06 45.33 2.73 0.00000 48.90 46.04 4.09 4.34 17 170 48.16 45.43 2.74 0.00000 48.99 46.13 4.08 4.34 18 180 48.27 45.52 2.74 0.00000 49.08 46.22 4.07 4.33 19 190 48.37 45.62 2.75 0.00000 49.18 46.31 4.07 4.32 20 200 48.47 45.72 2.75 0.00000 49.27 46.40 4.06 4.31 21 210 48.57 45.81 2.76 0.00000 49.36 46.49 4.05 4.30 22 220 48.67 45.90 2.76 0.00000 49.45 46.57 4.04 4.29 23 230 48.76 46.00 2.77 0.00000 49.54 46.66 4.04 4.29 24 240 48.86 46.09 2.77 0.00000 49.62 46.74 4.03 4.28 25 250 48.95 46.18 2.77 0.00000 49.71 46.82 4.02 4.27 PB-1 CRDM Reactor Trip NP.xls 37
)
Framatome ANP 32-501 9396-01 Table 7. Evaluation of CRDM Nozzle Corner Crack for Reactor Trip (Cont'd)
FRACTURE TOUGHNESS MARGINS Period of Operation: Time = 25.00 years Final Flaw Size: a= [ ] in. (after loss of load transient)
Margin = Kfa I KI(ae)
Loading Conditions RT1 RT2 Fracture Toughness, Kla 200.0 200.0 ksi'Jin KI(a) 48.95 46.18 ksiiin ae Kl(ae) 49.71 46.83 ksilin Actual Margin 4.02 4.27 Required Margin 3.16 3.16 PB-i CRDM Reactor Trip NP.xls 38
Framatome ANP 32-501 9396-01 Table 8. Evaluation of CRDM Nozzle Corner Crack for Loss of Flow INPUT DATA Initial Flaw Size: Depth, a =: ] in.
Material Data: Yield strength, Sy = 43.8 ksi Reference temp., RTndt = 60 F Upper shelf tough. = 200 ksiqin Kla = 26.8 + 12.445 exp [ 0.0145 (T - RTndt) ]
Kla is limited to the upper shelf toughness.
Applied Loads:
Loading Conditions LF1
- LF2**
Temperature (F) 528 612 Pressure, p (ksi)
Kla (ksiqin)
Position 200 200 x Hoop Stress (in.) (ksi) (ksi) 0.0000 0.2022 0.4043 0.6065 0.8087 1.1043 1.3999 1.6955 1.9911
- Loss of Flow Transient at 0.0403 hours0.00466 days <br />0.112 hours <br />6.66336e-4 weeks <br />1.533415e-4 months <br /> (max. stress)
- Loss of Flow Transient at 0.001 hours1.157407e-5 days <br />2.777778e-4 hours <br />1.653439e-6 weeks <br />3.805e-7 months <br /> (min. stress)
PB-1 CRDM Loss of Flow NP.xIs 39
Framatome ANP 32-5019396-01 Table 8. Evaluation of CRDM Nozzle Corner Crack for Loss of Flow (Cont'd)
STRESS INTENSITY FACTOR Kl(a) = 4(ita) [ 0.706(AO+Ap) + 0.537(2ahz)A 1 + 0.448(a 2 /2)A2 + 0.393(4a 3 /37ir)A 3]
where the through-wall stress distribution is described by the third order polynomial, S(x) = Ao + A1x + A 2x2 + A 3x3 ,
defined by:
Stress Loading Conditions Coeff. LF1 LF2 (ksi) (ksi)
A1 A2 A3 Effective crack size:
ae = a + 1/(6it)*[Kl(a)ISy] 2 Effective stress intensity factor:
Kl(ae) = 4(nae) [ 0.706(AO+Ap) + 0.537(2aeht)A, + 0.448(ae 2 /2)A 2 + 0.393(4ae 3 /3n)A 3 I PB-1 CRDM Loss of Flow NP.xls 40
Framatome ANP 32-5019396-01 Table 8. Evaluation of CRDM Nozzle Corner Crack for Loss of Flow (Cont'd)
FATIGUE CRACK GROWTH Transient
Description:
80 cycles over 40 years AN = 2 cycles/year Operating LF1 LF2 LF1 LF2 LF1 LF2 LF1 LF2 Time Cycle a KI(a) KI(a) AKI haae a, KI(aj) KI(a.) Margin = Kla / KI(aj)
(yr.) jin.) (ksiqin) (ksiqin) (ksi4in) (in.) (in.)
\ , \ , \ .
(in.)
(ksi~in)
, 5 .. .
(ksl~in) o 0 57.41 40.69 16.72 0.00012 59.22 41.54 3.38 4.81 1 2 57.56 40.83 16.73 0.00012 59.36 41.67 3.37 4.80 2 4 57.71 40.96 16.75 0.00012 59.49 41.81 3.36 4.78 3 6 57.86 41.10 16.77 0.00012 59.63 41.94 3.35 4.77 4 8 58.01 41.23 16.78 0.00012 59.76 42.06 3.35 4.75 5 10 58.16 41.36 16.80 0.00012 59.89 42.19 3.34 4.74 6 12 58.30 41.49 16.81 0.00012 60.02 42.32 3.33 4.73 7 14 58.44 41.62 16.82 0.00012 60.14 42.45 3.33 4.71 8 16 58.59 41.75 16.84 0.00012 60.27 42.57 3.32 4.70 9 18 58.73 41.88 16.85 0.00012 60.39 42.70 3.31 4.68 10 20 58.87 42.01 16.86 0.00012 60.51 42.82 3.31 4.67 11 22 59.00 42.13 16.87 0.00012 60.64 42.94 3.30 4.66 12 24 59.14 42.26 16.88 0.00012 60.75 43.07 3.29 4.64 13 26 59.28 42.38 16.89 0.00013 60.87 43.19 3.29 4.63 14 28 59.41 42.51 16.90 0.00013 60.99 43.31 3.28 4.62 15 30 59.54 42.63 16.91 0.00013 61.10 43.43 3.27 4.61 16 32 59.67 42.75 16.92 0.00013 61.22 43.55 3.27 4.59 17 34 59.80 42.87 16.93 0.00013 61.33 43.66 3.26 4.58 18 36 59.93 43.00 16.93 0.00013 61.44 43.78 3.26 4.57 19 38 60.05 43.12 16.94 0.00013 61.55 43.90 3.25 4.56 20 40 60.18 43.23 16.94 0.00013 61.65 44.01 3.24 4.54 21 42 60.30 43.35 16.95 0.00013 61.76 44.12 3.24 4.53 22 44 60.42 43.47 16.95 0.00013 61.86 44.24 3.23 4.52 23 46 60.54 43.59 16.96 0.00013 61.96 44.35 3.23 4.51 24 48 60.66 43.70 16.96 0.00013 62.06 44.46 3.22 4.50 25 50 60.78 43.81 16.96 0.00013 62.16 44.57 3.22 4.49 PB-1 CRDM Loss of Flow NP.xIs 41
Framatome ANP 32-501 9396-01 Table 8. Evaluation of CRDM Nozzle Corner Crack for Loss of Flow (Cont'd)
FRACTURE TOUGHNESS MARGINS Period of Operation: Time = 25.00 years Final Flaw Size: a= [ ] in. (after loss of load transient)
Margin = Kla / Kl(a)
Loading Conditions
_ LF1 LF2 Fracture Toughness, Kla 200.0 200.0 ksiVin Kl(a) 60.78 43.82 ksiin ae I KI(ae) 62.16 44.57 ksiVin Actual Margin 3.22 4.49 Required Margin 3.16 3.16 PB-i CRDM Loss of Flow NP.xs4 42
Framatome ANP 32-501 9396-01 Table 9. Evaluation of CRDM Nozzle Corner Crack for Loss of Load INPUT DATA Initial Flaw Size: Depth, a =E ] in.
Material Data: Yield strength, Sy = 43.8 ksi Reference temp., RTndt = 60 F Upper shelf tough. 200 ksiIin Kla = 26.8 + 12.445 exp [ 0.0145 (T - RTndt) ]
Kla is limited to the upper shelf toughness.
Applied Loads:
Loading Conditions LL1* LL2**
Temperature (F) 655 550 Pressure, p (ksi)
Kla (ksbiin)
Position 200 200 x Hoop Stress (in.) (ksi) (ksi) 0.0000 0.2022 0.4043 0.6065 0.8087 1.1043 1.3999 1.6955 1.9911 .-
- Loss of Load Transient at 0.00278 hours (max. stress)
- ' Loss of Load Transient at 0.0444 hours0.00514 days <br />0.123 hours <br />7.34127e-4 weeks <br />1.68942e-4 months <br /> (min. stress)
PB-1 CROM Loss of Load NP.xls 43
Framatome ANP 32-501 9396-01 Table 9. Evaluation of CRDM Nozzle Corner Crack for Loss of Load (Cont'd)
STRESS INTENSITY FACTOR KI(a) = 4 (na) [ 0.706(AO+Ap) + 0.537(2a/n)A1 + 0.448(a2 /2)A2 + 0.393(4a3 /3it)A 3 ]
where the through-wall stress distribution is described by the third order polynomial, S(x) = AO + Ajx + A2x2 + A 3x3, defined by:
Stress Loading Conditions Coeff. LL1 LL2 (ksi) (ksi)
AO At A2 A3 Effective crack size:
ae = a + 1I(67i)*[Kl(a)/Sy] 2 Effective stress intensity factor:
KI(ae) = 4(2tae) [ 0.706(AO+Ap) + 0.537(2ajht)A 1 + 0.448(ae2 /2)A2 + 0.393(4ae3 I/3i)A 3 ]
PB-i CROM Loss of Load NP.xIs 44
Framatome ANP 32-501 9396-01 Table 9. Evaluation of CRDM Nozzle Corner Crack for Loss of Load (Cont'd)
FATIGUE CRACK GROWTH Transient
Description:
80 cycles over 40 years AN = 2 cycles/year Operating LL1 LL2 LL1 LL2 LLI LL2 LL1 LL2 Time Cycle a Kl(a) KI(a) AKI Aa ae ae KI(a,) Kl(ae) Margin = Kla I KI(ae)
(yr.) (in.) (ksiqin) (ksi~n) (ksiqin) (in.) (in.) (in.) (ksi'in) (ksif1in) -
0 0 47.76 36.78 10.98 0.00004 49.23 37.27 4.06 5.37 1 2 47.93 36.88 11.06 0.00004 49.40 37.36 4.05 5.35 2 4 48.10 36.97 11.13 0.00004 49.57 37.45 4.04 5.34 3 6 48.27 37.06 11.21 0.00004 49.73 37.54 4.02 5.33 4 8 48.44 37.16 11.28 0.00004 49.90 37.63 4.01 5.32 5 10 48.61 37.25 11.36 0.00005 50.06 37.71 4.00 5.30 6 12 48.77 37.34 11.44 0.00005 50.22 37.80 3.98 5.29 7 14 48.94 37.43 11.51 0.00005 50.38 37.88 3.97 5.28 8 16 49.10 37.51 11.59 0.00005 50.54 37.97 3.96 5.27 9 18 49.27 37.60 11.67 0.00005 50.70 38.05 3.94 5.26 10 20 49.43 37.69 11.74 0.00006 50.86 38.13 3.93 5.24 11 22 49.59 37.77 11.82 0.00006 51.01 38.21 3.92 5.23 12 24 49.75 37.86 11.89 0.00006 51.17 38.29 3.91 5.22 13 26 49.91 37.94 11.97 0.00006 51.32 38.37 3.90 5.21 14 28 50.07 38.03 12.05 0.00006 51.48 38.45 3.89 5.20 15 30 50.23 38.11 12.12 0.00007 51.63 38.53 3.87 5.19 16 32 50.39 38.19 12.20 0.00007 51.78 38.60 3.86 5.18 17 34 50.54 38.27 12.27 0.00007 51.93 38.68 3.85 5.17 18 36 50.70 38.35 12.35 0.00007 52.08 38.75 3.84 5.16 19 38 50.85 38.43 12.42 0.00007 52.22 38.83 3.83 5.15 20 40 51.00 38.50 12.50 0.00007 52.37 38.90 3.82 5.14 21 42 51.15 38.58 12.58 0.00007 52.52 38.97 3.81 5.13 22 44 51.30 38.65 12.65 0.00007 52.66 39.04 3.80 5.12 23 46 51.45 38.73 12.73 0.00007 52.80 39.11 3.79 5.11 24 48 51.60 38.80 12.80 0.00007 52.94 39.18 3.78 5.11 25 50 51.75 38.87 12.88 0.00007 53.08 39.24 3.77 5.10 PB-i CRDM Loss of Load NP.xls 45
Framatome ANP 32-501 9396-01 Table 9. Evaluation of CRDM Nozzle Corner Crack for Loss of Load (Cont'd)
FRACTURE TOUGHNESS MARGINS Period of Operation: Time = 25.00 years Final Flaw Size: a= [ ] in.
Margin = Kla I KI(ae)
Loading Conditions LL1 LL2 Fracture Toughness, Kla 200.0 200.0 ksi'ln Kl(a) 51.75 38.87 ksinin ae KI(ae) 53.08 39.24 ksilin Actual Margin 3.77 5.10 Required Margin 3.16 3.16 PB- CRDM Loss of Load NP.xls 46
A M32-5019396-01 FRAMATOME ANP 7.0 Summary of Results a postulated large radial crack in A fracture mechanics analysis has been performed to evaluate the CRDM nozzle reactor vessel head the remnants of the original J-groove weld (and butter) at for the controlling transient.
penetration. Results of this analysis are summarized below Loss of Flow Temperature, T= 528 0 F Initial flaw size, ai= [ in.
Final flaw size after 25 years, af = [ ] in.
Flaw growth, af - aj = 0.192 in.
Stress intensity factor at final flaw size, KI = 62.16 ksi4in Fracture toughness, Kla = 200.0 ksiIin Safety margin: Kla / KI = 3.22 > 410 = 3.16 Conclusion alloy steel head, the above results Based on an evaluation of fatigue crack growth into the low J-groove weld would be acceptable demonstrate that a postulated radial crack in the Alloy 182 frequencies:
for 25 years of operation, considering the following transient Transient Frequency (cycles/year)
Heatup and Cooldown 5 Plant Loading and Unloading 75 10% Step Load Changes 50 50% Step Load Reduction 5 Reactor Trip 10 Loss of Flow 2 Loss of Load 2 47
A 32-5019396-01 FRAMATOME ANP 8.0 References
- 1. Framatome ANP Drawing 02-5019702E-2, "Point Beach Unit 1 CRDM Nozzle ID Temper Bead Weld Repair."
- 2. Framatome ANP Document 51-5017195-05, "Point Beach 1 & 2 CRDM Nozzle ID Temper Bead Weld Repair Requirements," September 2002.
- 4. Framatome ANP Document 51-5012047-00, "Stress Corrosion Cracking of Low Alloy Steel," March 2001.
- 5. (not used)
- 6. Framatome ANP Document 32-5020244-01, "Point Beach 1 CRDM Temperbead Bore Weld Analysis," February 2003.
Subject:
Dominion Engineering Calculations," September 2002.
- 8. ASME Boiler and Pressure Vessel Code,Section III, Rules for Construction of Nuclear Power Plant Components. Division 1 - Appendices, 1989 Edition with No Addenda.
- 9. ASME Boiler and Pressure Vessel Code,Section XI, Rules for Inservice Inspection of Nuclear Power Plant Components, 1998 Edition with Addenda through 2000.
- 10. Marston, T.U., 'Flaw Evaluation Procedures - Background and Application of ASME Section Xl, Appendix A," EPRI Report NP-719-SR, August 1978.
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