ML20087H551
| ML20087H551 | |
| Person / Time | |
|---|---|
| Site: | Palisades  |
| Issue date: | 04/20/1995 |
| From: | Killian D, Yoon K BABCOCK & WILCOX CO. |
| To: | |
| Shared Package | |
| ML18064A729 | List: |
| References | |
| 32-1235177, 32-1235177-00, NUDOCS 9505030330 | |
| Download: ML20087H551 (86) | |
Text
{{#Wiki_filter:. _____-_______ _ l ATTACHMENT 3 Consumers Power Company Palisades Plant Docket 50-255 FRACTURE MECHANICS ASSESSMENT OF PALISADES ALLOY 600 COMPONENTS BWNT CALC No. 32-1235177-00 April 24, 1995 ( 950503033o 950424 DR ADOCK 05000255 PDR
. _ -____________ ___ J
4 8WNT 20697-2 (91/89)
) (BWNP-20697 1)
C CALCULATION
SUMMARY
SHEET (CSS) ) s DOCUMENT IDENTIFIER 32-1238965-00 FM Assessment of Palisades Alloy 600 Components TITLE REVIEWED BY: PREPARED BY:
.E. Gian fo j / ,3 ,g K.K. Yoon NAME
#^ $1GNATURE
$1GNATURE T!?LE Principal Engineer - oxyg f!?obs r!Tte Techni nsultant o 2ONf 1
* ' V CoS7 CENTER 41020 REr. PAGE<S)
M TM STATEMENT: REVIEWER INDEPENDENCE, /> i' PURPOSE AND
SUMMARY
OF RESULTS: PURPOSE: 1 ne purpose of this analysis is to determine the suitability of Palisades Alloy 600 components for safe operation. Postulated internal axial and circumferential flaws are evaluated in accordance with the fracture toughness requirements set by the ASME Boiler and Pressure Vessel Code, Section XI, IWB-3612, considering the potential for crack growth and failure by net - section collapse (limit load). He objective is to develop a set of":rves from which the allowable time for continued service can be determined for a given flaw size. His is done by evaluar g both fatigue crack growth due to design cyclic loading and stress corrosion crack growth due to steady state stresses for t.ach of the Palisades' Alloy 600 components. i
SUMMARY
OF RESULTS: L j Table 6 shows the estimated remaining service life of the Palisades Alloy 600 components, assuming a constant through-wall stress equal to about 125% of the operating yield strength of the rnaterial. Rese results are graphically depicted in Figures 7 i i through 34. The pressurizer spray nozzle safe end has an estimated service life of 2.64 years assuming a worst case temperature of 640*F. The pressurizer temperature element '7zles can be expected to remain in service for about 7.5 years. i All other components can remain in service for 40 years. An alternate approach, based on the nonlinear distribution for residual axial stress in NUREG-0313, was used for the 4 pressurizer surge and spray nozzle safe ends. Rese results are shown in Table A 3 and Figures A-4 through A-6. He limiting service life was increased from 2.64 to 5.36 years for the pressurizer spray nozzle safe end at 640 F. l Note: This document is classified as BWNT Non-Proprietary. } 1 I 3 THE FoLLoWING COMPUTER CODES HAVE BEEN USED IN THIS DOCUMENT: CODE / VER$10N / REV CODE / VER$10N / REV THIS DOCUMENT c0NTAINS ASSUMPT!oNS THAT MUST BE VERIFIED prior TO USE ON SAFETY-RELATED WORK
' YES ( ) NOc X>
PAGE 1 oF 85
1 B&W NUCLEAR TECHNOLOGIES 32-1238965-00 l l RECORD OF REVISIONS j l l' : I L r Revision Descriotion of Revision pgg , O Original Release 4/95 s s l i l l i i I [ f I l l i L r I 1 l l l 1 ! Prepared by: D.E. Killian Date: 4/19/95 i i
. Reviewed by: K.K. Yoon Date: 4/20/95 Page 2 1 , . . _ , . - . _ _ _,
i j ' 4 : I B&W NUCLEAR TECHNOLOGIES 32-1238965-00: i i , TABLE OF CONTENTS i ; Section Title Page ; i List of Figures . . . . 4 t I List of Tables . . . . . . . . . 5 l 1 : Introduction .6 < i 1.0 . . . . . . . . l ) 1 2.0 Nozzle / Flaw Geometry . . 6 l . 2.1 Postulated Flaw Geometries 6 j
. . . . . 3 2.2 Geometry of Alloy 600 Components . . . . . 9 i
- 10 3.0 Stresses . . . . . . . . .
4 3.1 Applied Stresses . . . . . . 10 3.2 Spectrum History 10 { i j 4.0 Fracture Mechanics Analysis . . . . . . 11 ! l 4.1 ASME B&PV Code, Section XI, Acceptance Criteria . . . 11 { 4 4.2 S'.ress Intensity Factor Solutions . . . . 12 , 4.3 Irwin Plasticity Correction . . . . . . 15 ! 4.4 Limit Load Solutions . . . . . . 17 l ' i 4.5 initial Flaw Depth . . . . . . 19 j 4.6 Fatigue Crack Growth .
. . . . . . 20 4.7 Stress Corrosion Crack Growth . . . . . . 22 l
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i ' 5.0- Material Properties . . . . . . . 25 , j 6.0 Procedure for Assessment of Alloy 600 Components . . . 26 l 7.0 Results and Conclusions . . 28 ) l . . . . . i i-j 8.0 References . . . . . . . . 58 Appendix
.A Alternate Method using Residual Stress Distribution from NUREG-0313 . 59
! B Verification of FORTRAN Programs . . . . . 71
- C Computer input Files . . . . . . . 79 D List of Computer Output Microfiche . . . . . 85 4 i l
1 1 j Prepared by: D.E. Killian Date: 4/19/95 1 Page 3 Reviewed by: K.K. Yoon Date: 4/20/95
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i l B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 [ LIST OF FIGURES .j l Figure Title Page a Semi-Elliptical Internal Axial Flaw 7 l 1. Semi-Elliptical Internal Circumferential Flaw 8 j 2.
- 3. 'Ihe Irwin Plastic Zone Correction. -16
- 4. Inconel - Wrought Material - EEct of Temperature and PWR Environment on Fatigue Crack Growth Rates 21 Comparison of Crack Growth Rates as a Function of Temperature ' 24
- 5. {
- 6. Procedure Used to Evaluate the Remaining Service Life of Each \
of the Palisades' Alloy 600 Components - 27 I Allowable Flaw D*h Versus Time to Failure: Yield Stress. Axial Flaw !
- 7. Pressurizer TE Nozzles 30 :
- 8. Pressurizer Surge Nozzle Safe End 31 l
- 9. Pressurizer Spray Nozzle Safe End @ 540 deg F 32
- 10. Pressurizer Spray Nozzle Safe End @ 640 deg F 33 ;
- 11. Hot Leg Surge Nozzle Safe End 34
- 12. Hot Leg Shut Down Nozzle Safe End 35
- 13. Hot Ieg Loop Drain Nozzle 36
- 14. Hot Leg Pressure & Sampling Nozzle 37
- 15. Hot Leg RTD Nozaje 38 ,
- 16. Cold Leg Shut Down Nozzle Safe End 39
- 17. Cold Leg Spray Nozzle 40
- 18. Cold Leg Charging and Loop Drain Nozzles 41
- 19. Cold Leg Pressure & Sampling Nozzle -42
- 20. Cold Leg RTD Nozzle 43 A))gwable Flaw Death Versus Time to Failure: Yield Stress. Cire Flaw
- 21. Pressurizer TE Nozzles 44 j
j 22. Pressurizer Surge Nozzle Safe End 45 a 23. Pressurizer Spray Nozzle Safe End @ 540 deg F 46 i' 24. Pressurizer Spray Nozzle Safe End @ 640 deg F 47
- 25. Hot Leg Surge Nozzle Safe End 48
- 26. Hot Leg Shut Down Nozzle Safe End 49 l 50
- 27. Hot Leg Loop Drain Nozzle
- 28. Hot Leg Pressure & Sampling Nozzle 51 j 29. Hot Leg RTD Nozzle 52 l 30. Cold leg Shut Down Nozzle Safe End 53
- 31. Cold Leg Spray Nozzle 54 1 32. Cold Leg Charging and Loop Drain Nozzles 55 4 33. Cold Leg Pressure & Sampling Nozzle 56 j j 34. Cold Leg RTD Nozzle 57 l d
i s i l Prepared by: D.E. Killian Date: 4/19/95 l Reviev ed by: K.K. Yoon Date: 4/20/95 Page 4
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i l
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l i 32-1238 % 5-00 B&W NUCLEAR 'ECHNOLOGIES I LIST OF TABLES } Title Page Table l
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Summary of Geometric Dimensions for Palisades' Alloy 600 Components 9 ;
- 1. i Axial Flaw Shape Factors Associated with the Deepest Point on the Flaw 12 ;
2a. - 13 2b. Axial Flaw Shape Factors Associated with the Point Near the Surface
- 3. Circumferential Flaw Shape Factors Associated with the Deepest Point 14 l on the Flaw l,
- 4. Derivation of Paris Law Coefficients Using Data from Figure 4 for a ,
20 : PWR environment ! Material Properties Required for Fracture Mechanics Assessment 5. of Palisades' Alloy 600 Components 25 l i Summary of Time to Failure for an Initial Flaw Depth of 0.010" 29 6. Summary of Allowable Flaw Depths for One Fuel Cycle (18 months) 29 {
- 7. i.
l l l l l l I l i l I i ( Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 5 i
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i B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 l 1.0 Introduction The purpose of this analysis is to determine the suitability of Palisades Alloy 600 components for safe operation. Postulated internal axial and circumferential flaws are evaluated in accordance with the fracture toughness ; i requirements set by the ASME Boiler and Pressure Vessel Code, Section, XI, IWB-3612, considering the potential for crack growth and failure by net section collapse (limit load). The objective is to develop a set of i curves from which the allowable time for continued service can be determined for a given flaw size. This is ; done by evaluating both fatigue crack growth due to design cyclic loading and stress corrosion crack growth due to steady state stresses for each of the Palisades' Alloy 600 components. 2.0 Nozzle / Flaw Geometry 2.1 Postulated Flaw Geometries in this analysis, a postulated semi-elliptical internal surface flaw is evaluated with a longitudinal orientation and with a circumferential orientation. As will be seen in Section 4.3, the postulated axial flaw will be evaluated using a third sder curve fit of the circumferential stress, while the circumferential flaw will be evaluated using a third order curve fit of the axial stress. Figures 1 and 2 graphically depict the information required to evaluate the postulated flaws. l l l l , i I l
- . l l
1 l l Prepared by: D E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon - Date: 4/20/95 Page 6
B&W NUCLEAR TECHNOL,0GIES 32 1238 % 5-00 w == 2c Centerline Figure 1. Semi-Elliptical Internal Axial Flaw Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 7
i i B&W NUCLEAR TECHNOLOGIES 32-1238965-00 i i V l a/ f V \ 2c/ ni ' Ro l l 1 l l J L 3rd Order Polynomial ! Curve Fit of Axial Stress
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, r i Figure 2. Semi-Elliptical Internal Circumferential Flaw Prepared by: D.E. K.illian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 8 i
l B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 2.2 Geometry of Alloy 600 Components i 4 The pertinent geometric dimensions are given below in Table 1. i Table 1 Summary of Geometric Dimensions for Palisades' Alloy 600 Components (Ref.1)
.I Nonle/ location Quantity OD ID Penetration l Safe End (in.) (in.) Weld I TE-0101 and Pressurizer I cach 1315 0.815 Partial TE-0102 Spray Nonle Safe Pressurizer 1 4.500 3.692 Full End Surge Nonle Safe Pressurizer 1 12.750 10.740 Full End Surge Nozzle Safe Hot Leg Piping i 13.000 10.741 Full ;
End Shut Down Cooling Hot Leg Piping i 12.750 10.741 Full l Outlet Nozzle Safe . End I Loop Drain Nozzle Hot Leg Piping i 2375 1.689 Full i Shut Down Cooling Cold Leg Piping 4 13.000 10.741 Full Inlet Nozzle Safe ! End Pressure & Hot Leg Piping 10 1.250 0.625 Full Sampling Nozzle RTD J-Weld Nozzle Hot Leg Piping 10 1.250 0377 Partial Spray Line Outlet Cold Leg Piping 2 3.500 2.693 Full Nozzle Charging Nozzle Cold Leg Piping 2 2375 1.689 Full Loop Drain Nozzle Cold Leg Piping 4 2375 1.689 Full Pressure A Cold Leg Piping 8 1.250 0.625 Full Sampling Nozzle RTD J. Weld Nozzle Cold Leg Piping 12 1.250 0377 Partial Prepared by: D.E. Killian Date: 4/19/95 ; Reviewed by: K.K. Yoon Date: 4/20/95 Page 9 f l i
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B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 l 1 3.0 Stresses 3.1 Applied Stresses ] l De actual stress distribution for each of the components studied is unknown. However, certain conservative assumptions can be made to ensure that stresses used in predicting the remaining service life of the Palisades l i Alloy 600 components bound the actual stresses l ne effects of primary stresses, operating stress and geometrical anomalies (i.e. the distonion of TE-0102 during the weld repair process), along with the weld residual stress could produce extremely high stresses ne welding , j process without a post weld treatment may leave a large residual stress. Since no evaluation was perfonned to estimate the magnitude of the residual stress, it is postulated that the residual stress is equal to the material yield l strength. De material yield stmngth at room temperature will be used to develop residual stresses at operating temperatures. Based on tabulated yield strengths from Section III of ASME Code, room temperature yield ; strengths are about 125% of yield strengths at operating temperatures above 500F. It is therefore appropriate and j conservative to use room temperature yield strength as the postulated total stress. In the present analysis, this . l stress will be applied as a constant through-wall stress in both the axial and circumferential directions. l 1 he degree' of conservatism associated with the above approach varies from nozzle to nozzle, but can best be characterized by categorizing the nozzles into two main groups according to the type of attachment weld, J- < groove partial penetration or full penetration. Nozzles attached to PCS components by J-groove type welds l (Pressurizer TE nozzles and PCS Loop RTD nozzles) are not connected to any type of extemal piping. His in ] tum virtually eliminates the potential for circumferential PWSCC, since there is no axial stress to either initiate l or drive a crack. On the other hand, circumferential PWSCC may very well be the primary mode of felure for , full penetration type nozzles with girth buu welded safe ends. For this category, hieb 'esidual axial stresses may j be present at the location of the girth butt weld, and additional operational loads are produced by the attached 1 piping. At the same time, compressive circumferential stress at the root of the weld, typical of butt welded l piping components, would tend to decrease the likelihood of axial PWSCC. Recognizing that the potential for PWSCC varies for these two types of welded nozzles (partial and full penetration), it is nevenheless both conservative and convenient to evaluate all nozzles for both axial and circumferential failure modes. Based on research conducted on large diameter BWR stainless steel piping, it may be particularly conservative to assume a constant value of through-wall axial stress for evaluating girth butt welded safe ends. NUREG-0313 (Ref.10) presents a nondimensional, nonlinear through-wall stress distribution for axial residual stresses in 12" diameter piping joined by girth butt welds. Although this fonn of residual stress distribution may not be exactly applicable to weld between small diameter piping and nozzle safe ends, it could be somewhat representative of the actual stress distribution, and as such, is used as an altemate method of aulysis in Appendix A. l 1 3.2 Spectrum History i The Palisades plant has 500 heatup and cooldown design cycles (Ref.1). In calculating fatigue crack growth, the maximum stress (i.e. yield strength) is combined with the minimum stress (i.e. zero at shutdown) to determine a cyclic stress range. It should be noted that the amount of fatigue crack growth was found to contribute only about 1% of the total crack growth as compared to PWSCC. For this reason, and based on experience, it was ; determined that accounting for smaller transients in the fatigue crack growth analysis for these components was not needed. For stress corrosion crack growth at a given location, the maximum stress state (i.e. toom i temperature ylsid strength) is used to evaluate the corrosion crack growth within a given time span. Predictions of yearly crack growth are based on 12.5 heatup/cooldown cycles per year (500 cycles over a 40 year design life). Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 10
32-1238 % 5-00 B&W NUCLEAR 'IT.CHNOLOGIES 4.0 Fracture Mechanics Analysis - A linear elastic fracture mechanics analysis is performed to determine the maximum allowable flaw size that meets IWB 3612 fracture toughness margins and that the assumed semi-elliptical internal surfice crack does not grow to through wall. As previously noted, a semi-elliptical internal surface flaw with a longitudinal orientation and with a circumferential orientation will be used as the postulated defects. The following sections outline the fracture mechanics methodology used in this analysis. 4.1 ASME B&PV Code, Section XI, Acceptance Criteria A flaw is acceptable if the applied stress intensity factor satisfies the following IWB-3612 criterion (Ref. 4) for l normal and upset conditions: K,(a)< K,~ [10 , i whem: Kfa)r = the maximum applied stress intensity factor for normal and upset conditions based on ; final crack depth. l K, = crack arrest fracture toughness for the corresponding crack tip temperature. l Since the highest possible stress is being employed in this analysis, the normal / upset and emergency / faulted ! conditions would use the same stress value for determination of the applied stress intensity factor. Also, as will , be demonstrated in Section 5.0, the crack arrest fracture toughness, K., and the crack initiation fracture ! toughness, Ku, are the same for this application. Hence, the only difference in the N/U and E/F conditions is in : the fracture toughness margins required in IWB-3612. Since the fracture toughness margin is higher in the N/U l condition /10) than in the E/F condition M2), the N/U condition is the bounding criteria j for satisfying IWB 3612. j i l l l l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 PageiI f l 1
d l l 32-1238 % 5-00 B&W NUCLEAR 'ECHNOLOGIES 4.2 Stress Intensity Factor Solutions AXIAL FLAW l j Maximum Death Point: De Mode I stress intensity factor for the deepest point on the semi-elliptical flaw is (Ref. 3): 3 l K,=(xt)'5[{ o,G,] I o-o L where o, are the coefficients of the stress polynomial describing the hoop stress (c) variation through the cylinder wall and are defined below. , a=o,+ o, (z/t) +o, (z/t)2 + c3 (z/t)' z is the distance measured from the inner surface of the cylinder wall and t is the cylinder wall thickness. He l l G, are the shape factors associated with the coefficients of the stress polynomial and may be expressed by the 2 l following general form: G, = A, + (A,a, + A3 a,8 + A3 a,8 + A4 a,' + A,a/) / [0.102(R/t) - 0.02]* - a, = (a/t)/(a/c)" ne values of A, through As and m are given in Table 2a. He R, is cylinder inner radius. De 2c and a are the f flaw length and flaw depth at the deepest point of the flaw respectively. l Table 2a. Axial Flaw Shape Factors Associated with the Deepest Point on the Flaw (Ref. 3) i A. A, A, A3 A. A3 m ; l G, 0.0 1.7767 -2.5975 2.7520 -1.3237 0.2363 0.58 G, 0.0 0.1045 0.4189 0.000 0.0 0.0 0.22 G3 0.0 0.02038 .00397 0.42126 0.0 0.0 0.10 G3 0.0 0.07283 .36006 0.66883 0.0 0.0 0.05 l l l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 12
i i I I 32-1238965-00 i B&W NUCLEAR TECHNOLOGIES l I , I ! AXIAL FLAW l Point Near Surface: ne Mode I stress intensity factor for the point near the surface on the semi-clliptical flaw is (Ref. 3): 3 K,=(st)"[{ o,G,j o.o where G,i = G * [A. + A,(a/t)2] (a/c)' he G,, are the shape factors associated with the point near the surface of the flaw, ne G, are the shape factors associated with the deepest point on the flaw, defined on the previous page, he A., A, and r are defined in l Table 2b. Table 2b. Axial Flaw Shape Factors Arsociated with the Point Near the Surface (Ref. 3) i l A. A, r l G, 1.06 0.28 0.4I l G,i 0.25 0.20 0.26 i
\
G,2 0.07 0.16 0.06 j l G,3 0.085 0.02 0.0 I l t l l l I l l l l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 13 l
B&W NUCLEAR TECHNOLOGIES 32-1238965-00 CIRCUMFERENTIAL FLAW ne Mode I stress intensity factor for the deepest point on the semi-elliptical flaw is (Ref. 3): 3 K,=(st)as[{ q(a/t)'G,]
#o where o, are the coefficients of the stress polynomial describing the axial stress (c) variation through the cylinder wall and are defined below, o=o,+ oi (z/t) +o, (z/t)2 + o3 (z/t)'
1 z is the distance measured from the inner surface of the cylinder wall and t is the cylinder wall thickness. He l G, are the shape factors associated with the coefficients of the stress polynomial and may be expressed by the following general form: . G, = Ai a, + A2 a,' + A a,' + A.a,' + A3 a/ + A a (R/t - 5) 3 ai = (a/t)/(a/c)" He values of A, through A, and m are given in Table 3. De R is the mean radius of the cylinder. He 2c and j - a are the flaw length measured at the cylinder inner surface and flaw depth at the deepest point of the flaw, ; j respectively. I Table 3. Circumferential Flaw Shape Factors Associated with the Deepest Point on the Flaw (Ref. 3) i A, A A3 A. A3 A. m j G. 1.8143 -1.9881 1.4382 -0.4680 0.056696 0.0067 0.50 G, 1.0959 -0.9874 0.5399 -0.09303 0.0 0.0 0.38 G 1.1836 -2.3347 2.9756 -1.7652 0.39483 0.0 030 G3 1.0029 -2.0160 2.5627 -1.4951 032759 0.0 0.25 Note: A. is set equal to zero for R/t < 5. l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 14 _ - _ __ .. - - - - . ~ . _ _.
l ! i B&W NUCLEAR'iECHNOLOGIES 32 1238 % 5-00 4.3 Irwin Plasticity Correction < Linear clastic stress analysis of sharp crack-like defects predicts infinite stresses at the crack tip. However, in i real materials, stresses at the crack tip are finite because the crack tip radius is finite. To account for crack tip plasticity, a simple estimation of the elastic-plastic boundary is made using the elastic stress analysis. This approach is called the Irwin plasticity correction and is applicable up to the point where moderate crack tip j yielding occurs l i l When yielding occurs, stresses must redistribute in order to satisfy equilibrium. De shaded region in Figure 3 bounded by the yield stress and the clastic stress field curve represents forces that would be present in an elastic material but cannot be carried in the elastic-plastic material because the stress cannot excud yield. De plastic j zone must increase in size to accommodate these forces. Note that the redistributed stress in the elastic region is ; higher than clastic only stress, implying a higher effective stress intensity factor. Irwin accounted for this increase in K by defining an effective crack length that is slightly longer than the actual crack size. He found that a good approximation cf K,, can be obtained by placing the tip of the effective crack in the center of the ! l ; l plastic zone. Thus, the effective crack length is defined as the sum of the actual crack size and a plastic zone correction: , a4 =a+r, Under plane strain conditions, this effective increase in crack length is defined by (Ref. 9): j l 1 I (n-1) K/a)), r r#- 1+(P/P)2 6n (n+1)( rs o ! where: P = Applied load i P, = Limit load i n = strain hardening coefficient : Kfa) = stress internity factor based on actual crack length ! ay, = yield stress l I ne effective stress intensity factor is then obtained by inserting a,,into the K cxpression for the geometry of l I interest. l l l l l l Prepared by: D E. Killian Date: 4/19/95 ( Reviewed by: K.K. Yoon Date: 4/20/95 Page 15 f
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B&W NUCLEAR TECHNOLOGIES 32-1238965-00 l Opening Stress Elastic Yield Stress
'\. Elastic-Plastic
= ,, .. /
Y
-y ry l Figure 3. The Irwin Plastic Zone Correction l
1 Prepared by: D.E. Killian Date: 4/19/95 i Reviewed by: K.K. Yoon Date: 4/20/95 Page 16
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l i l B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 4.4 Limit Load Solutions I In addition to failure by brittle fracture, a net section collapse failure needs to be assessed The safest approach j in a fracture mechanics assessment is to adopt an analysis that spans the entire range from linear elastic to fully l plastic behavior. Such an analysis accounts for the two extremes of brittle fracture and plastic collapse. ( i AXIAL FLAW - Internal, Senal-Elliptical Longitudinal Flaw l The limit load pressure, p., for an internal, semi-elliptical longitudinal flaw is calculated by (Ref. 3): i i t 1-x I P,* 9 ? 0,, y, 1_ X
- M ?
i i a x=- t i f t y, 1.61c 2 3 Rt- , i Up,. "
%u * %=ma 2 '
r i R, + R* R= i 2 i where a = the crack depth, , c = half the crack length l and t = the cylinder wall thickness. The design pressure, p,, for all the Palisades' Alloy 600 components examined is 2500 psi. (Ref.1) Since no margin of safety is applied to the limit load condition, the component will not fail by plastic collapse if . i 4
)
Ps < P, 1 Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 17
B&W NUCLEAR TECHNOLOGIES 32-1238965-00 CIRCUMFERENTIAL FLAW l Two limit load solutions are used for the cin:umferential flaws, ne solution for a internal, semi-elliptical l circumferential flaw is used for nozzles with R/t 2 5. A more conservative solution for a internal,360* , circumferential flaw is used for R/t < 5, where the semi-elliptical flaw solution is not valid. l Since external piping loads are not generally available for these nozzles, the limit load solutions for circumferential flaws will be conservatively compared to an applied axial load that is equivalent to a constant , through-wall axial stress equal to the material yield strength at operating temperature; that is, r P, < P, i where 4 P, = a,, x (R,' - R,') l Internal, Semi-Elliptical Circumferential Flaw Limit Load Solution I ne limit load solution for an internal, semi-clliptical circumferential flaw is (Ref. 3): , P, = 2xRtaj ,,[ 2a/n -(x0'n)(2 - 2q + xq)/(2 - q)] l where a = arc cos(A sin i 0) , 2 j' , x [(1 -Q(2 -2q +xQ + (1 -q +xQ j 2 [ l + (2 -q)(1 -Q ) e x=1 1 0= I A R, t 5
- R, l
l l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 18 I
l 32-1238965-00 B&W NUCLEAR TECHNOLOGIES Internal,360* Circumferential Flaw Limit Load Solution he limit load solution for an internal,360* circumferential flaw is (Ref. 3): P, = rJj ,,, [R,2 - (R, + a)2) 6 The particular limit load solution used for each nozzle is listed below, based on the R/t ratio. Nozzle BJ Limit Load Solution Pzr TE-0101 and TE-0102 2.63 360* uniform depth Pn Spray SE 5.57 semi-elliptical flaw Pzr Surge SE 634 semi-elliptical flaw HL Surge SE 5.75 semi-elliptical flaw HL Shut Down SE 635 semi-elliptical flaw HL Loop Drain 3.46 360* uniform depth CL Shut Down SE 5.75 semi-elliptical flaw HL Pressure & Sampling 2.00 360* uniform depth HL RTD 1.43 360* uniform depth j CL Spray 434 360* uniform depth CL Charging 3.46 360* uniform depth l CL Loop Drain 3.46 360* uniform depth l CL P essure & Sampling 2.00 360* uniform depth CL fsTD 1.43 360* uniform depth 4.5 Initial Flaw Depth he leading industry thoughts on the initiation crack size is that machining or fabrication process leaves a thin layer of high residual stress at the surface. Some quantitative measurements have been made using the X-ray , diffraction technique followed by hardness tests. Boursier (Ref. 2) has shown the existence of a residual stress field up to a depth of 0.003 inch. Measurements taken from the mockups of Alloy 600 nozzles indicate that the highest residual stress occurs at 0.002 inch; however, it could reach 50 ksi at about the 0.010 inches, depending on the surface finish. An initial crack size of 0.010 inch will be used for the crack growth analysis. l l l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K K. Yoon Date: 4/20/95 Page 19 l
i B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 4.6 Fatigue Crack Growth i De fatigue crack growth due to design cyclic loading was calculated using the Paris Law, similar to that given in Article A-4000 of Section XI of the ASME Boiler and Pressure Vessel Code (Ref. 4), ! da
= C(AK)"
# i i
where C and n are dependent on the material and environmental conditions, and AK is the difference between K ! due to the maximum primary stress and K due to the minimum primary stress. De minimum primary stress is 0 l psi at shutdown, hence, AK is the K due to maximum primary stress. De fatigue crack growth rate data (da/dN) for Alloy 600 in' a PWR environment can be seen in Figure 4. De { coefficients for the Paris crack growth law are derived in Table 4. j I Table 4. Derivation of Paris Law Coefficients Using Data from Figure 4 for a PWR Environment l i; da ;
= C(AK)"
I dN : da ! log (dN) = logC + n(log (AK)) t l da/dN AK da/dN AK (mm/ cycle) (MPs/m) (in/ cycle) (ksVin) 6.706E-4 30 2.640E-5 27.30 j 1.724E-4 20 6.g00E-6 18.20 t l i l Setting up two equations for two unknowns: ; I l -4.5785= log C + 1.436 n ,
-5.4048= log C + 1.266 n i ne required coefficients are:
I ! C = 4.09E-10 I n = 3.349 for use with units ofinches and ksVin. l I l \ l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by:,K.K. Yoon Date: 4/20/95 Page 20 ' J 1 I
2 l B&W NUCLEAR TECHNOLOGIES 32-1238965-00 g
- INCONEL l
wrought material ! R = 0.1 10-3 - _ G
- o
- 1 w
u L o 4 6 o ! N E 6 o i A n i E A o 2'10-4 1 L,
- Lo
! N m Ao e m
- 10'5 _ o -
4 ! A PWR environment. f = 4 epm i A cir . 8 = 320 *C . f = 10 Hz o air . R.T. f =10 Hz i i 4 - l t i l 10 e i i 20 . 30 40 50 60 70 80 AK,MPa /iii 1 Figure 4. Inconel- Wrought Material- Effect of Temperature and PWR Environment on Fatigue Crack
- Growth Rates (from Reference 5) i i Prepared by
- D.E. Killian Date: 4/19/95 Reviewed by: K K. Yoon Date: 4/20/95 Page 21
l B&W NUCLEAR TECHNOLOGIES 32-1238965-00 4.7 Stress Corrosion Crack Growth The corrosion crack growth was calculated using Scott's (Ref. 6) model with an activation energy of 33 Kcal/ mole. This crack growth rate model was developed based on industry data for the stress corrosion cracking of Alloy 600 steam generator (SG) tubing. This model is considered the most conservative model available for Alloy 600 PWSCC on SG tubing. An appropriate temperature correction is incorporated to account for the difference in operating temperature between the different Alloy 600 components and SG tubes. Scott's crack growth rate equation for 330*C (626*F) is:
$ = C,(K,-K,)"sec "
dt where n = 1.16 Ku = 9 MPa/m is assumed K, - applied stress intensity factor, in units of MPa/m C, (330 C) = 2.8e-12 This equation includes a factor of five to account for the effect of cold work on crack growth rate. It should be noted that an explicit threshold stress intensity factor is required before crack propagation occurs in this correlation. In order to permit investigation of shallow flaws, a correlation based on the original Scott model was developed without the r - Lt threshold. It is the following relation that will be utilized in this analysis: b = D,(2.89E-13 K/")'
- dt sec where Ki = applied stress intensity factor, in units of MPa/m, and 1.0 s x = 1.3539(K,)*"
1 i and D, is the temperature correction parameter. The Alloy 600 components operate at a temperature of $40*F in the cold leg piping,590*F in the hot leg piping and 640*F in the pressurizer (Ref.1). Since it is well known that crack growth rate is strongly affected b-j temperature, a temperature adjustment for analysis of the Alloy 600 components is necessary. A temperature correction was obtained from laboratory and field data for SCC growth rates for Alloy 600 in primary water environments. An activation energy of 33 Kcal/ mole for crack growth was used to adjust crack growth rate for i the different operating temperatures, as shown below. Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 22
B&W NUCLEAR TECHNOLOGIES 32-1238 % 5 00 i da/dt (Operating Temperature) = da/dt (Test Temperature - 330"C)
- D, I
( ) D=# ; ( ) {
.e ,
t where Q = 33 Kcal/ mole = 138.072 Kjoules/ mole , R = 8.3143 joules /K-mole
= Test Temperature !
T, T = Operating Temperature of the Alloy 600 Component l i The temperature adjusted crack growth rates utilized in this analysis for Alloy 600 components are: b = 1. 41973 (2. 89E-13 K/'y * @ 640"F I dt sec i l b = 0.38902 (2.89E-13 K/y * @ 590*F . dt sec ! l l l l l b = 0.09365 (2.89E-13 K/~*y * @ 540*F dt sec r Figure 5 illustrates the temperature dependance of these PWSCC crack growth equations, along with P. Scott's j original curve. In English units, these equations are: b = 55.895 (3.386E-13 K/'y #" @ 640*F l \ dt sec b = 15.316 (3.386E-!3 K/'y '" @ 590"F dt sec b = 3.687 (3.386E-13 K/'y '" @ 540"F dt sec where Ki = applied stress intensity factor, in units of ksh/in, and x is defined as above. l Prepared by: D.E. Killian _ Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 23
l B&W NUCLEAR TECHNOLOGIES 32-1238965-00 Cosspadson of Crack Growth Rate Models for ABoy 600 at Various Tesaperatures I ' I 1E4 : !
- l
! 1E-9 :- 5
/s e,W 1E 10 - '
f
/ P Scott 4,g..Q @626 F D..O O..Q O, ..Q -@'+
IL11 ; - 5 , 9..O ,g - BWNT
@626 F Q
O '
^ 1E-12 m ,'.'
j ! BWNT f . l .
~
Q @640 F L
~ ~ ~ ~
c IE-13 '-- . l E
- BWNT
- .' @MF l -e-1E-14 p ) BWNT 5 @540 F i . '.'
l _
, .. 4. .
IL15 [,-
~M l IL16 g
' ' ' ' I ' ' A"-
IL17 i I 0 20 40 60 30 100 j KI(MPani) l l l Figure 5. Comparison of Crack Growth Petes as a Function of Temperature l l l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 24 1 i
l B&W NUCLEAR TECHNOLOGIES 32-1238965-00 5.0 Material Properties ! All components examined are made of Alloy 600 (Ref.1). He code flaw evaluation procedure, IWB 3612, is based on linear clastic fracture mechanics. In this application for Alloy 600 at a temperature above 500*F, this material is very ductile and no cleavage fracture um occur. In ; l this evaluation, equivalent K, and K, values are derived Jg value from a J-resistance curve. Ju is defined as the l initiation point of ductile tearing, J being at J, level. De Ju is converted to K3by the following equation in a LEFM frame of definition: K, = [Ju /(1-v E 2
)]"2 in addition, observing that ductile tearing can not be sustained l without increasing crack driving force, K 3value obtained from this relationship can be considered as a crack l arrest toughness in the absence of additional crack driving force. Herefore,3K = K, = K,.
He fracture toughness, J,, for Alloy 600 was from Table 3 of Ref. 7. For unirradiated specimens tested at 2 427 C (800*F), J, was 575 kJ/m2 , and at 24*C (75*F) J, was 382 kJ/m . Using linear interpolation and the plane strain correlation, the fracture toughness is evaluated at 540 F (hot leg piping),590*F (cold leg piping), and 640*F(pressurizer). The fracture toughness utilized in each component is shown below in Table 5. He following table summarizes the Alloy 600 material properties required for the fracture mechanics assessment. Table 5. Material Properties Required for Fracture Mechanics Assessment of Palisades' Alloy 600 Components Ultimate Operating i Yield Ku ID Component Stress Stress Temp (ksi) (ksi) (*F) (ksiV'in) j [Ref. l] [Ref. l] [Ref.1] [Ref. 7) i 1 Pu TE-0101 46.2 98.2 640 310.18 1 1 Pu TE-0102 46.2 98.2 640 310.18 l 2 Pn Surge SE $1.2 100.3 640 310.18 l 3 Pn Spray SE (Note 1) 77.5 114.0 540 302.33 l 4 640 310.18 l 590 306.28 I 5 HL 5;rge SF 51.2 100.3 6 HL She Down SE 51.2 100.3 590 306.28 7 HL Lc.r; Drain 37.1 93.2 590 306.28 8 F. ss a Sampling 39.8 94.7 590 306.28 9 i,L e ;D 48.0 99.0 590 306.28
.O f.. Fu' Down SE 51.2 100.3 540 302.33 11 0 6pe 37.1 93.2 540 302.33 12 C1. e.g e . 37.1 93.2 540 302.33 i 12 01. 1.o m '> rain 37.1 93.2 540 302.33
" CL t.z:,s & Sampling 39.8 94.7 540 302.33 14 CL RTD 48.0 99.0 540 302.33 Note 1: The correct value of normal spray flow is critical to the PWSCC assessment. For flows of 50 to 70 gpm it is can be assumed that the safe end temperature is equal to the cold leg temperature (540*F). If the flow is only 1.5 gpm, the flow is too low to cool the safe end and an assumed temperature equal to the pressurizer temperature (640*F) is required (Ref.1). To perform a bounding assessment, an analysis will be completed at both temperatures for the pressurizer spray nozzle safe end.
Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 25
p_ _ . _ . . . i B&W NUCLEAR TECHNOLOGIES 32 1238 % 5-00 6.0 Procedure for Assessmen of Alloy 600 Components I Based on information depicted in the previous sections, two FORTRAN programs, AX.F and CIRC.F were f created to evaluate the remaining service life of each of the Palisades' Alloy 600 components assuming both an l axial flaw and a circumferential flaw. Figure 6 presents a logic diagram for these programs. , i ne BWNT administrative procedure for preparing engineering calculations (Ref,11) permits the use of computer programs written for execution on personal computers, provided the programs are documented and i verified. De program listings for AX.F and CIRC.F can be found in Appendices B and C, respectively, of , Reference 15, the proprietary version of the present fracture mechanics assessment. Both programs are verified j in Appendix B of this document. He input files uW with programs AX.F and CIRC.F are listed in Appendix C of this document. The output f files are contained in Reference 15 in the form of computer output microfice. Dese files are listed in Appendix j t D of this document. , I l l I i I l l l l 1 l l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/93 Page 26 l, l ___ _ , , _ _ - , . _ , , - _ - - . . .m> <
B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 i + , i l w,ut irsdal Depm O = 0.010' and i Flow Aspect Railo (2f1 Af1,6/1) j l Inpd Through-war Stees Diettuton
-^ '
and Operaung Temp of e-- l k Compute Kmetfog(a) Used for FCG Kmeteoc(a) Used for SCC l Compute Umit Load Check N43812 FT Margin l Not Sadened and Umit Load Margin I Saliened l Compute FCG daK(Kmax fo0(a))*n i CompmosCC dao=D(E*Kmax ecc(a)*F)*G'1/12.5yr, l Compum ; a = a + def + dec j e = Aspect Rado/2
- a 1 NO Last Fad 0ue Cycle YES stop Figure 6. Procedure Used to Evaluate the Remaining Service Life of Each of the Palisades' Alloy 600 Components Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 27
B&W NUCLEAR TECHNOLOGIES 32-1238965-00 l I i 7.0 Results and Conclusions ] Table 6 shows the estimated remaining service life of the Palisades' Alloy 600 components. Rese results are graphically depicted in Figures 7 through 34. General Observations o ne amount of fatigue crack growth as compared to stress corrosion cracking is extremely small. j (Fatigue crack growth accounts for approximately 1% of total crack growth) o Figures 7 through 20 (Axial) and 21 through 34 (Circumferential) demonstrate the allowable flaw size for each of the components for both axial and circumferential flaws. His is primarily intended to serve as an acceptance criteria in the event that a flaw is found in one of the components during an inspection. If the flaw is below the time-to-failure curve for the required length-to-depth ratio, the flaw is acceptable for the next fuel cycle. Table 7 contains the allowable flaw depths that can be justified for one fuel cycle (18 months) of continued operation. o Nozzles attached to PCS components by J-groove type welds (Pressurizer TE nozzles and PCS Loop RTD nozzles) are not connected to any type of external piping. His in turn virtually eliminates the potential for circumferential PWSCC, since there is no axial stress to either initiate or drive a crack. On the other hand, circumferential PWSCC may very well be the primary mode of failure for full penetration type nozzles with girth butt welded safe ends. For this category, high residual axial stresses may be present at the location of the ginh butt weld, and additional operational loads are produced by the attached piping. At the same time, compressive circumferential stress at the root of the weld, typical of butt welded piping components, would tend to decrease the likelihood of axial PWSCC. Component Specific Observations o ne wall thickness of the pressurizer temperature element nozzles is only 0.25". Hence, if any flaw exists that is exposed to the primary water, PWSCC may be a significant concern. Still, for the conservative length-to-depth ratio of 6, it would take about 7.5 years for an axial flaw and 13 years for a circumferential flaw to grow to a critical size. o Of all the components examined in this study, only the pressurizer surge nozzle has undergone post-weld heat treatment (Ref.1). To be conservative, the yield stress was still utilized for the stress distribution for this component. Even still, the remaining service life of this component exceeds the design life of the plant. o As previously reported, the assumed temperature of the pressurizer spray nozzle safe end is extremely important for a PWSCC assessment. (ne SCC growth rate differs by a factor of 15 between 540*F (Cold Leg) and 640"F (Pressurizer).) If the temperature is assumed to be that of the cold leg, the component should be able to remain in-service without failure for about 35 years. However, if the pressurizer temperature is used, the component could only be expected to last less than 3 years. o All other components can be expected to remain in service for 40 years without failure. Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 28
B&W NUCLEAR TECHNOLOGIES 32-1238965-00 Table 6. Summary of Time to Failure for an Initial Flaw Depth of 0.010" Note: Total through-wall stress distribution set equal to room temperature yield strength. Axial Flaw Circumferential Flaw Component Thick. Time to Failure (years) Time to Failure (years) ID 1/a=2 1/a=4 1/a=6 1/a=2 1/a=4 1/a=6 l (in.) 1 Pn TE-0101 0.25 40.00 20.16 7.68 40.00 32.48 13.04 i Pu TE-0102 0.25 40.00 20.16 7.68 40.00 32.48 13.04 2 Pu Surge SE 1.005 40.00 40.00 40.00 40.00 40.00 40.00 3 Pn Spray SE @S40'F 0.404 40.00 40.00 35.12 40.00 40.00 40.00 4 0.404 37.12 632 2.64 38.64 8.00 3.60
@640*F 5 HL Surge SE 1.1295 40.00 40.00 40.00 40.00 40.00 40.00 6 HL Shut Down SE 1.0045 40.00 40.00 40.00 40.00 40.00 40.00 7 HL Loop Drain 0343 40.00 40.00 40.00 40.00 40.00 40.00 8 HL Press & Sampling 03125 40.00 40.00 40.00 40.00 40.00 40.00 9 HL RTD 0.4365 40.00 40.00 40.00 40.00 40.00 40.00 10 CL Shut Down SE l.1295 40.00 40.00 40.00 40.00 40.00 40.00 11 CL Spray 0.4035 40.00 40.00 40.00 40.00 40.00 40.00 12 CL Charging 0343 40.00 40.00 40.00 40.00 40.00 40.00 12 CL Loop Drain 0343 40.00 40.00 40.00 40.00 40.00 40.00 13 CL Press & Sampling 03125 40.00 40.00 40.00 40.00 40.00 40.00 14 CL RTD 0.4365 40.00 40.00 40.00 40.00 40.00 40.00 Table 7. Summary of Allowable Flaw Depths for One Fuel Cycle (18 months)
Notes: 1. Total through-wall stress distribution set equal to room temperature yield strength.
- 2. Flaw depths are in inches.
Axial Flaw Circumferential Flaw ID Component Thick. Allowable Flaw Depth Allowable Flaw Depth (in.) 1/a=2 1/a=4 1/a=6 1/a=2 1/a=4 1/a=6 1 Pu TE-0101 0.25 0.065 0.035 0.020 0.050 0.030 0.025 1 Pn TE-0102 0.25 0.065 0.035 0.020 0.050 0.030 0.025 ; 2 Par surge SE 1.005 0.270 0.135 0.075 0.270 0.145 0.085 l 3 Pn Spray SE @540*F 0.404 0.285 0.215 0.155 0320 0.270 0205 ) 4 6640 F 0.404 0.035 0.015 0.010 0.035 0.020 0.015 5 HL Surge SE 1.1295 0.645 0.470 0320 0.775 0.550 0390 6 HL Shut Down SE 1.0045 0.605 0.435 0300 0.680 0.510 0365 7 HL Loop Drain 0343 0.255 0.200 0.165 0.170 0.155 0.140 8 HL Press & Sampling 03125 0.215 0.165 0.135 0.155 0.135 0.125 9 HL RTD 0.4365 0.265 0.185 0.130 0.200 0.170 0.150 10 CL Shut Down SE 1.1295 0.835 0.695 0.520 1.015 0.810 0.630 11 CL Spray 0.4035 0360 0330 0305 0.235 0.230 0.225 12 CL Charging 0343 0305 0280 0.260 0.205 0.200 0.195 12 CL Loop Drain 0343 0305 0280 0260 0.205 0.200 0.195 13 CL Press & Sampling 03125 0.275 0.250 0.230 0.190 0.185 0.180 14 CL RTD 0.4365 0375 0325 0.255 0.260 0.250 0.240 Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 29
32-1238965-00 i Time to Failure vs. Initial Flaw Size 40 - l- .g 1 . . .- 1/a = 2 35 - ! ! k. ll' " 4
! I.
- 1 ....... Ila = 6 30 - .
t.
; t.
t.
; n j 25 - ;
. i.
b I, I. E : I, 2 20 - ;
*n .
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0 . O O.02 0.04 0.06 0.08 0.1 Initial Flaw Size (inches) l l Figure 7. Time to Failure for Pressurizer TE Nozzles. i Axial Semi-Elliptical inside Surf ace Flaws with Constant Through-Wall Yield Stress l Page 30 i l
1 32-1238965-00 l Time to Failure vs. Initial Flaw Size I 40 -
-r. . s.
; I I l - - - - l/a = 2 l I I 35 - '
- I 1/a=4 i ; .
f
. l ...... 1/a = 6 30 - . I.
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=
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O - i ' O O.05 0.1 0.15 0.2 0.25 0.3 0.35 initial Flaw Size (inches) Figure 8. Time to Failure for Pressurizer Surge Nozzle Safe End: Axial Semi-Elliptical Inside Surface Flaws with , Constant Through-Wall Yield Stress ! Page 31 l l
32-1238965-00
)
i i Time to Failure vs. Initial Flaw Size AO '
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* \
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i ' \ 0 0.05 o,s o.15 O.2 o.25 o,s initial Flaw Size (inches) i i I l Figure 9. Time to Failure for Pressurizer Spray Nozzle Safe End at 540F: i Axial Semi-Elliptical Inside Surf ace Flaws with Constant Through-Wall Yield Stress Page 32
, _ , _ ._ 4 ' " ' ' "'
I t 32-1238965-00 I e Time to Failure vs. Initial Flaw Size i 1 40 - is.
\
\. _ _.-lla=2 '
I 35 - t, lla=4 i I. ...... 1/a = 6 i I. , 6 30 -
- t. -
1 i I 3 25 - I. 3 :
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i .,.. ......%.% ._._._._._._._._ 0 . , . - - . ' ' O 0.01 0.02 0.03 0.04 0.05 0.06 initial Flaw Size (inches) j Figure 10. Time to Feature for Pressurizer Spray Nozzle Safe End at 640F: Axial Serni-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress l Page 33
32-1238965-00 ! t
?
r Time to Failure vs. Initial Flaw Size . 40 . t
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O 0.1 o.2 O.3 0.4 O.6 0.6 03 initial Flaw Size (inches) Figure 11. Time to Failure for Hot Leg Surge Nozzle Safe End: Axlal Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 34
i 32-1238965-00 1 l l 6 Time to Failure vs. Initial Flaw Size , \
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i \ 40 *i'I.
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32-1238965-00 Time to Failure vs. Initial Flaw Size i so - * \
\.
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0 . . . . . . 0 0.05 0.1 0.15 0.2 0.25 0.3 Initial Flaw Size (inches) Figure 13. Time to Failure for Hot Leg Loop Drain Nozzle: Axlal Semi-Elliptical Inside Surface Flaws with Constant Through-Wall Yield Stress Page 36
i 32 1238965-00 Time to Failure vs. Initial Flaw Size I t AO - -
\, (
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. ,,,..\le*2 36 ~
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0 . . . ' 0 0.05 0.1 0.15 0.2 0.25 Initial Flaw Size (inches) Figure 14. Time to Failure for Hot Leg Pressure & Sampling Nozzle: Axial Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 37
l 32-1238965-00 l I Time to Failure vs. Initial Flaw Size : 40 - - g
\,
' \ g . ~ . . \la . 2 35 - h i
. 't. ' lle = 4 t
- t
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0 * ' ' ' ' 0 0.05 o.1 0.15 O.2 O.25 O.3 Initial Flaw Size (inches) i Figure 15. Time to Failure for Hot Leg RTD Nozzle: Axial Semi-Elliptical inside Surface Flaws with Censtant Through-Wall Yield Streso Page 38 i
1 ! l 32-1238965-00 l l ! Time to Failure vs. Initial Flaw Size l l i 40 - - r- - - .- l
. t.
- I t - - - 1/a = 2 .
35 - 'g l . 1/a=4
. t.
l 1, 1/a = 6
. t 30 - ;
'g
. t.
- t -
n
- E 25 -
't.
g . \ e .
\.
. \.
* \
. 20 - ., i
- u. '. i 1 \
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., s., ,
., s 1
. \
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. r.
., s.
., s i,
5- .. .
.. . 's.,
.s r.~.
0 . , , , . , , , ..............'l 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Initial Flaw Size (inches) Figure 16. Time to Failure for Cold Leg Shut Down Nozzle Safe End: Axlal Semi-Elliptical inside Surface Flaws with ! Constant Through-Wall Yield Stress Page 39 1 l i
32 1238965-00 :
?
Time to Failure vs. Initial Flaw Size 40 - . , I. i.
. i. - - . - 1/a = 2 !
- 1 35 - -
; t, 1/a=4 .
- 1 g ...... 1/a = 6 30 - ;. \,
; \
- - \
- s.
25 - .
. \. .
\
D *
. 'g 2 i* i
- j 20 - ., i, 4
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N
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., ., .. - s '
..,....,s 0 . . . . . . . . '.
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 initial Flaw Size (inches) Figure 17. Time to Failure for Cold Log Spray Nozzle: Axial Semi-Elliptical Inside Surface Flaws with Constant Through-Wall Yield Stress Page 40
i 32-1338965-00 Time to Failure vs. Initial Flaw Size 40 - . 1 t
'. \*
!. 1
- - - - 1/a = 2 35 - l 'g 1/a=4
=
- t. ~ ~
*
- lla = 6
. \.
30 - , i.
\.
. \.
\.
# 25 - '.
\.
E . e . s. t > , '
. \
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.] 20 - ',,
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. N, s.
., s.
5- 5.. N. N. l l
' .. ...' *.,- s.
..,..7 o . . . . .
o 0.05 0.1 0.15 0.2 0.25 0.3 initial Flaw Size (inches) Figure 18. Time to Failure for Cold Leg Charging and Loop Drain Nozzles: Axial Semi-Elliptical inside Surf ace Flaws with Constant Through-Wall Yield Stress Page 41 l
32-1238965-00 i . l l l Time to Failure vs. Initial Flaw Size I l ' l l l 40 - - i - . i
. t.
I. - - - - 1/a = 2 l 35 - i.
; \ 1/a = 4
- ; t. - - - l/a = 6 ,
. \
30 - I, g l
- t. '
l :
\'
E 25 - ; \. I e . g 2 .
\
g . \
- 2 E
20 - 5 '\.
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\,
. \
s 10 - ', s.
, s.
., s,
, s
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j 5- s -
' .,' ... 's, ;
s s-
....~
0 . . . . . . 0 0.05 0.1 0.15 0.2 0.25 0.3 Initial Flaw Size (inches) Figure 19. Time to Failure for Cold Leg Pressure & Sampling Nozzle: Axial Semi-Elliptical inside Surf ace Flaws with l Constant Through-Wall Yield Stress Page 42
i i 1 . 1 I 32-1238965-00 i Time to Failure vs. Initial Flaw Size 40 - , - . I : I l }
- - - - 1/a = 2 35 - g 1/a = 4 I.
g ...... 1/a = 6 , 1 ! 30 - l
- l a 1
( :
\.
- t F
g 25 - a i
\.
- g e.
. s '
( 2 : \ > 3 e '
- g 20 - ; i l
l i o
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A i
., N,
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. s
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s.,
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..... ...,~. i o , , , , , ,
l 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 f initial Flaw Size (inches) i Figure 20. Time to Failure for Cold f.eg RTD Nozzle: Axial Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress l Page 43
l 1 32-1238965-00 I i 1 f Time to Failure vs. Initial Flaw Gize 40 - -.
\. N
{ i - - - - 1/a = 2 { 35 - '
; I. 1/a=4 )
I.
; g l/a = 6 I
30 - i .
. I.
. I.
g E 25 - : . . i t e . 2 : 1 E
- s k. i'
=e 20 - .
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o 1 e ; I E p: 15 - ; 1,
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. .~. . . _ '. ~. *: : - : .-- - _ -
0 . . . . . . . ; O 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Initial Flaw Size (inches) Figure 21. Time to Failure for Pressurizer TE Nozzles: Circumferential Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 44 i i l l
32-1238965-00 l i Time to Failure vs. Initial Flaw Size 1 1 40 - -r ! t.
. t. l I
- . - - 1/a = 2 35 - l I >
l j 1/a = 4
; I .....- 1/a = 6 l
30 - l .
. I
. l I.
E 25 - ! e
- i.
e ;
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.'.................~. . . .~. . ......-. .
O . . . . . . . 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 initial Flaw Size (inches) Figure 22. Time to Failure for Pressurizer Surge Nozzle Safe End: Circumferential Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 45
32-1038965-00 F j Time to Failure vs. initial Flaw Size i ; i. 40 ' N ,\ i
\. , , . . tia ,2 I.
35 - '. \
\l6*
, l
\ , g
- ..-....\ts**
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 initial Flaw Size (inches) Figure 23. Time to Failure for Pressurizer Spray Nozzle Safe End at 540F: l Circumferential Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 46 i
32-1238965-00 i Time to Failure vs. Initial Flaw Size 40 - p,N. I i - . - - 1/a = 2 35 - l, ife ,4 i g ...... 1/a = 6 3 30 - ! I.
, i.
- , t E 25 - < e ; e , I. !
>= .
{ e
!! i E
- g 20 - i i-
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0 . . . . . . 0 0.01 0.02 0.03 0.04 0.05 0.06 Initial Flaw Size (inches) Figure 24. Time to Failure for Pressurizer Spray Nozzle Safe End at 640F: Circumferential Semi-Elliptical Inside Surf ace Flaws with Constaat Through-Wall Yield Stress Page 47
32-1238965-00 l 1 Time to Failure vs. Initial Flaw Size 40 t T.
- t.
, . , . . \la 2
'. \.
35 - '. \. ' tla a 4
* \.
1 ....... tle - 6
\
30 - .*
, 'g
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3,25-t, E . t
,be 5 '.'.\.
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' }
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\
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to - * 's N., 5-
= ,'
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. . . . . . ...........-;*~~~m.. . . . . . . . . . . . . . .. . . . . .
0 . . . . , ' 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 initial Flaw Size (inches) l l Figure 25. Time to Failure for Hot Leg Surge Nozzle Safe End: Circumferential Semi-Elliptical Inside Surface Flaws with Constant Through-Wall Yield Stress i Page 48
32-1238965-00 l Time to Failure vs. Initial Flaw Size 40 - , \. t
'. \
,. . . . tle = 2 \
\
35 - \
. . \ls*#
\
. 1
'. .......tls'6
. \.
30 - t
*\.
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\
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\
1
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5- ..,
~*'~._.~_-.,
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O . . . . , ' ' O O.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Initial Flaw Size (inches) Figure 26. Time to Failure for Hot Leg Shut Down Nozzle Safe End: Circumferential Semi-Elliptical inside Surf ace Flaws with Constant Through-Wall Yield Stress Page 49
j 32 1238965-00 i 4 Time to Failure vs. Initial Flaw Size 40 ' 8
. - '\.
- \
i . \ , ,. . \la ,2 i ss - '. \
- ila
- A i
. \
s
. ....-.. gla
- 6
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se ~ . .. g i
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0 , , , , , , , , , . . . . . , , 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Initial Flaw Size (inches) Figure 27. Time to Failure for Hot Leg Loop Drain Nonte: Cirecmferential Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 50 1
1 32-1238965-00 Time to Failure vs. Initial Flaw Size 40 - .
~
. t I
l - - - - 1/a - 2 35 - I. g 1/a = 4
$ I. ** ~~~~ lla = 6
- I 30 - : l
. i.
l t
!! 25 - ;
e . I. I. : I.
- I g :
1
.]
u. 20 - : l t o ' i 1 E 15 - i: ;
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0 . . . . . . . . . . . . . . 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 initial Flaw Size (inches) Figure 28. Time to Failure for Hot Leg Pressure & Sampling Nozzle: Circumferential Semi Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 51
a 32 1238965-00 l Time to Failure vs. Initial Flaw Size l l 1 40 - * , , \
., \, . \
s
* \ i
'g -."..gla.2 \
ss - * , gg . A
'. \.
\ 1
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O , , , , , , , , , O 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 initial Flaw Size (inches) , 1 Figure 29. Time to Failure for Hot Leg RTD Nozzle: Circumferential Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 52
32-1238965-00 Time to Failure vs. Initial Flaw Size 40 7 - 3,
- i
. t. - - - - 1/a = 2 ,
- - t 35 -
1, lla = 4 i l l/a = 6
. i.
1 30 - I.
= t.
t.
. t.
2 25 - I 1 e ; e . s. b i S.
? -
o .
\
g 20 - ., i E ; \ o i. 8 . \. E - s 15 - s, p .,
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s. s 10 -
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5-
.. ~ r ~.
..,.... ~. ,~
0 . . . . . . . , . . . , . , . , . 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Initial Flaw Size (inches) Figure 30. Time to Failure for Cold Leg Shut Down Nozzle Safe End: Circumferential Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 53
32-1238965-00 , Time to Failure vs. Initial Flaw Size , i 40 - , , g
; 1
- - - t/a = 2 i
- t. j 35 - .
. t. 1/a=4
; 1
; 1, l/a = 6 30 - *
\.
. \.
; 5 2 25 -
\g >
I i lt i.
\
e - i
'\
5 - +
=e 20 - -
- u. '.'.
\. -
O
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e '
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\,
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10 - ., 's -
., s
., 's
., 's '
5- .
'.,'.s,
.s.%.
..\,
0 . . . . . 0 0.05 0.1 0.15 0.2 0.25 initial Flaw Size (inches) Figure 31. Time to Failure for Cold Leg Spray Nozzle: Circumferential Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 54
32-1238965-00 l l Time to Failure vs. Initial Flaw Siza 1 40 - .
- 1 !
. t l
. t - - - - 1/a = 2 ;
35 - !
, I. 1/a = 4 I I t
*
- lla = 6 30 - : 1,
; 1 I. t. ,
- t 2 25 - .
a e a. t. e D
'. \.
E '. o . \. =o 20 - ', \. - E . \
& '. '\
e '. . i , E p 15 -
., \, ;
, s
. s.
. \'
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s-5- '.,
's s-
.. . s
. ,',s ,
o . . . . . . . . . l 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 Initial Flaw Size (inches) Figure 32. Time to Failure for Cold Leg Charging and Loop Drain Nozzles: Circumferential Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 55
l l 32-1238965-00 l l l l l i l Time to Failure vs. Initial Flaw Size i ! 40 - . 1 l ;
,\ '. - l
' ; i
; - - - 1/a = 2 35 - I '
; 1/a = 4 t.
l
. \ ...... 1/a = 6 >
l . . l 30 - ; *
. I.
; 1
\.
2 25 - - t. ! e ; . e . t. b
- s E t ,
a ' e 20 - '.
. \.
S I
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\,
N,
, s
's, 10 - '.-
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N,
, s N
's, s,
5- ' .. ,* N. s
.,'**.s's
,,..,s, 0 . . . . . . . . . .
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 ; l Initial Flaw Size (inches) l i Figure 33. Time to Failure for Cold Leg Pressure & Sampling Nozzle: Circumferential Semi-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 56
1 32-1238965-00 1 i Time to Failure vs. Initial Flaw Size 40 - ,1 -g* i 1 - - - - 1/a = 2 35 - I I J. I/a=4
. 1 l/a = 6
. I.
- 1 30 - ;
1 i
' ; 1 i 1 2 25 - '.
e e i.
> , . t.
\
e Ei '.
's
=e 20 - -
- u. *
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o
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e .
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. . ,, s ,
O , , , , , , , , , , , 0 0.020.050.07 0.1 0.120.150.17 0.2 0.220.250.27 i 5 5 5 5 5 5 initial Flaw Size (inches) Figure 34. Time to Failure for Cold Leg RTD Nozzle: Circumferential Fami-Elliptical inside Surface Flaws with Constant Through-Wall Yield Stress Page 57 4
I B&W NUCLEAR TECHNOLOGIES 32-1238965-00 8.0 References
- 1. BWNT Document 51-1235040-00, " Alloy 600 Program - Inputs."
- 2. Boursier, J., et al., " Stress Corrosion Cracking of Alloy 600 in Water: Influence of Strain Rate on the Different Stages of Cracking," EUROCORR '92, June 1992.
- 3. Zahoor, A., " Ductile Fracture Handbook", EPRI-Report NP-6301-D, Electric Power Research Institute, Palo Alto, CA,1990.
- 4. ASME Boiler and Pressure Vessel Code, Seu XI,1986 Edition.
- 5. Amzallag, C., Baudry, G. and Bemard, J.L., IAEA Specialists Meeting on Suberitical Crack Growth, Freiburg, West Germany, May 13-15,1981, p. 229.
- 6. Scott, P.M., "An Analysis of Primary Water Stress Corrosion Cracking in PWR Steam Generators,"
Presented at the OCED Meeting, Brussels, Belgium, September 16-20, 1991.
- 7. Mills, W.J., " Fracture Toughness of Two Ni-Fe-Cr Alloys," Hanford Engineering Development Laboratory Document HEDL-SA-3309, April 1985.
- 8. Anderson, T.L., " Fracture Mechanics: Fundamentals and Applications," CRC Press, Boca Raton, FL, 1991.
- 9. Kumar, V., et. al, "An Engineering Approach for Elastic-Plastic Fracture Analysis," EPRI NP-1931, July 1981. l
- 10. Hazelton, W.S. and Koo, W.H., " Technical Report on Material Selection and Processing Guidelines for BWR Coolant Pressure Boundary Piping," Final Report, NUREG-0313, Rev. 2, January 1988.
I 1. BWNT Procedure BWNT-0402-01, Rev. 29, " Preparing and Processing BWNT Calculations," June 1, 1994. )
- 12. ASME Boiler and Pressure Vessel Code, Section 111,1986 Edition.
- 13. CPCo Document P-MECH-CALC-021, Rev. O, " Stress and Fatigue Evaluation of the Pressurizer Surge i
Nozzle for Consumers Power Company, Palisades Nuclear Plant."
- 14. CPCo Document EA-SP-03361-01, Rev. 4, " Pipe Stress Analysis for Pressurizer Spray System Piping."
- 15. BWNT Document 32-1235177-00, "FM Assessment of Palisades Alloy 6 r O mponents" (BWNT Proprietary).
References 13 and 14 are not available for entering into the BWNT Record Center tm may be referenced as permitted by BWNT procedure BWNT-0402-01, Appendix 2. 'Ihese documents are available through CPCo. 1 Approval:D - pV g[& & Y. R.R. Steinke Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K K. Yoon Date: 4/20/95 Page 58
B&W NUCLEAR TECHNOLOGIES 32-1238965-00 Appendix A Attemate Method using Residual Stress Distribution from NUREG-0313 A.1 Analytical Procedure Recognizing that the use of a constant through-wall stress distribution for axial residual weld stresses is conservative for the evaluation of circumferential flaws in girth butt welded components, an altemate method is utilized in this appendix to take advantage of a postulated nonlinear stress distribution at two nozzle locations, the pressurizer surge and spray safe end to attached piping welds, nis technique incorporates the nondimensional form of through-wall stress distribution found in NUREG-0313 (Ref.10) for axial stress, described by the founh order polynomial: 4 olo, = [ o, 41, 1-0 where: o, = 1.0 o, = -6.910 a=2 8.687 c3 = -0.480 o, = -2.027 4 = x/t a, = stress magnitude at 4 = 0 (inner surface) ne material yield strength at operating temperature serves as a good estimate of the inner surface residual stress. Although operating stresses would add directly to residual stresses in a purely linear analysis, the total is limited by clastic-plastric material behavior. To account for some strain hardening, but still control the magnitude of the total stress, through-wall stresses are limited to 125% of the operating temperature yield strength. Since a maximum constant through-wall stress condition is not being used to evaluate circumferential flaws, the normal condition fracture toughness acceptance criterion no longer inherently bounds the faulted condition criterion. His requires that the faulted condition fracture toughness acceptance criterion must now be checked at each crack depth, along with the normal condition criterion. Table A-1 presents the complete procedure used to incorporate the NUREG-0313 stress distribution in the determination of acceptable circumferential flaw sizes for the pressurizer surge and spray nozzle safe ends. De four major steps of this procedure are: (1) check normal condition fracture toughness, (2) check faulted condition fracture toughness, (3) check for net section collapse (limit load), and (4) calculate incremental crack growth. The first five substeps of Step 1 are executed in Table A-2 for three configurations: the pressurizer surge nozzle safe end at 640 'F, and pressurizer spray nozzl: safe end at 540 'F and 640 'F. His ponion of the procedure computes s-tress coefficients used with the third order polynomial stress intensity factor solution of Section 4.2. A graphical representation of the generation of this third order curve is shown in Figures A-1 through A 3 for the three nozzle configurations. De remaining portion of the evaluation procedure outlined in Table A 1 has been programmed in the FORTRAN code CINLF, listed in Appendix D of Reference 15. Program CINL.F is verified in Appendix B. Input data is contained in Appendix C. Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 59
B&W NUCLEAR TECHNOLOGIES 32-1238965-00 Table A-1. Flaw Evaluation Procedure for Use with the NUREG-0313 Residual Stress Distribution Sten 1 - Check normal condition fracture touchness
- 1. Calculate a constant through-wall primary plus secondary operating stress using Equation (10) from Section NB-3653 of the ASME Boiler and Pressure Vessel Code (Ref.12). His equation includes contributions from intemal pressure, external piping moments and thermal discontinuity between the Alloy 600 safe end and stainless steel piping. The resultant extemal piping moment is derived from deadweight and thermal loads.
- 2. Calculate through-wall axial residual stresses using NUREG-0313's nondimensional fourth order form with the inside surface stress set equal to the material yield strength at operating temperature.
- 3. Calculate the sum of the founh order residual stress and the constant through-wall operating stress.
- 4. Limit this total stress to 125% of the operating temperature yield strength.
- 5. Fit a third order polynomial curve to the data points corresponding to the " cutoff" total stress at operating temperature.
- 6. Calculate a normal condition stress intensity factor using the solution described in Section 42 for a semi-elliptical circumferential flaw.
- 7. Evaluate the IWB-3612 normal condition fracture toughness criterion (Ref. 4):
Kfa) < Ku /VIO Step 2 - Check faulted condition fracture touchness
- 1. Calculate a constant through-wall axial stress for faulted conditions using ASME Code Equation (10) considering design pressure, deadweight plus thermal plus safe shutdown earthquake (SSE) seismic loads, and thermal discontinuity.
- 2. Calculate a faulted condition stress intensity factor and evaluate the IWB-3612 faulted condition fracture l
- toughness criterion (Ref. 4):
Kfa) < K /V2 Steo 3 - Check for net section collapse (limit load)
- 1. Calculate an equivalent axial pipe load from the constant through-wall axial stress computed in Step 2.1 for faulted conditions: l P=oum% n ( R,2 - R2i )
- 2. Calculate the limit load using the solution in Section 4.4 for semi-elliptical circumferential flaws.
- 3. Check that the axial pipe load from Step 3.1 is less than the limit load.
Steo 4 - Calculate incremental crack crowth
- 1. Using stresses calculated in Step 1, calculate fatigue crack growth for up to 500 heatup and cooldown cycles and stress corrosion crack growth for an equivalent, incremental time span.
Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 60
l t 32-1238965-00 ! l l l Table A-2. Derivation of Nonlinear Stress Distributions ' i I Stresses from Piping Equation No.10 , S = C1 *(p Do)/(2 t) + C2*Do/(2 l)*M + C3*E_ab'l alpha _a - alpha _bl
- delta _T l C1 = 1.0 Material "a" = A600 safe end C2 = 1.0 Material "b" = 316 SS pipe C3 = 0.6 l
l Pzr Surge Pzr Spray Pzr Spray ; 1
@ 640F @ 540F @ 640F Do 12.750 4.500 4.500 in ,
Di 10.740 3.692 3.692 in t 1.005 0.404 0.404 in , 1 644.27 11.01 11.01 in*4 l alpha _a 7.87E-06 7.75E-06 7.87E-06 /F A600 alpha _b 9.66E-06 9.49E-06 9.66E-06 /F SS _ l 3.08E+07 3.08E+07 3.08E + 07 psi - A600 @ RT per ASME Code E_a 2.81 E + 07 2.81 E + 07 2.81 E + 07 psi SS @ RT per ASME Code l E_b ! E ab 2.95E+07 2.95E +07 2.95E+07 psi Avg. RT value
)
1 Normal Conditions 570 470 570 F (T - 70F) j delta _T p 2205 2205 2205 psi _ l M 832.74 43.10 43.10 in-kip (DW + Thermal) (*) j S 40286 35562 39147 psi ! Faulted Conditions delta _T 570 470 570 F (T - 70F) l 2500 2500 psi l p 2500 M 1500.80 138.46 138.46 in-kip (DW + Thermal + SSE) (*) S 48768 56691 60275 psi l i I Note
- References for applied piping moments are:
Pzt Surge Nozzle - Ref.13 Pzr Spray Nozzle - Ref.14 l l l Page 61 i
- - _ _ . . . . . . _ ~ .-. .-. . _ _ _ _ . . _
i l t 32-1238965-00 l l { Table A 2. Derivation of Nonlinear Stress Distributions (Cont'd) Axial Residual Stresses from NUREG-0313 i l S = .Si
- SUM ( SJ
- Xi'J ), j = 0,1,2,3,4 i
where: SO = 1.000 and XI = x/t S1 = -6.910 . Si = stress at XI=0 (inner surface) i S2 = 8.687 3 S3 = -0.480 Let Si = Oper. Temp. Yield Strength . f S4 = -2.027 j Pzr Surge Pzr Spray Pzr Spray ;
@ 540F -@ 640F Residual Stress Plus l
@ 640F Normal Operating Stress, psi l Si, psi = 40200 62900 60900 ;
Pzr Surge Pzr Spray Pzr Spray f XI S, psi @ 640F @ 540F @ 640F 0.00 40200 62900 60900 80486.2 98462.27 100046.5 j 0.05 27181.02 42529.51 -41177.22 67467.23 78091.78. 80323.74 j 0.10 15886.53 24857.28 24066.91 56172.73 60419.55 63213.43 i 0.15 6283.716 9831.983 9519.36 46569.92 45394.25 48665.88 l l 0.20 -1672.45 -2616.84 -2533.63 38613.75 32945.43 36612.89 j l 0.25 8039.21 -12578.8 -12178.8 32246.99 22983.5 26967.71 ; 0.30 -12886.1 -20162.5 -19521.4 27400.15 15399.76 19625.1 i O.35 -16294.7 -25495.9 -24685.2 23991.53 10066.37 14461.3 0.40 -18359 -28725.9 -27812.5 21927.22 6836.394 11334.03 0.45 -19185.1 -30018.5 29064 21101.07 5543.738 10082.47 l 0.50 -18891.5 -29559.1 -28619.2 21394.72 6003.202 10527.33 ! 0.55 -17608.6 -27551.8 -26675.8 22677.57 8010.456 12470.76 0.60 -15479.4 -24220.2 -23450.1 24806.82 11342.05. 15696.42 ) 0.65 -12658.8 -19806.9 -19177.1 27627.44 15755.4 19969.44 0.70 -9314.05 -14573.5 -14110.1 30972.16 20988.8 25036.44 0.75 -5624.7 -8800.84 -8521 34661.5 26761.43 30625.52
- 0.80 -1782.44 -2788.94 -2700.26 38503.77 32773.33 36446.26 l 0.85 2008.827 3143.165 3043.224 42295.03 38705.44 42189.74 l 0.90 5532.939 8657.26 8381.99 45819.14 44219.53 47528.51
! 0.95 8561.528 13396.02 12970.08 48847.73 48958.29 52116.6 t 1.00 10854 16983' 16443 51140.2 52545.27 55589.52 i l l l I l l Page 62 l -_ _ _ . . . _ __ _ _ - , ._ - . _ -
l 32-1238965-00 Table A-2. Derivation of Nonlinear Stress Distributions (Cont'd) j Residual Stress Plus Normal Operating 125% Oper. Temp. Yield, psi Stress with Cutoff at 125% Operating Pzr Surge Pzr Spray Pzr Spray Temperature Yield Strength 50250 78625 76125
]
Res + Opr Stress, psi Res + Opr Stress w/ Cutoff, psi Pzr Surge Pzr Spray Pzr Spray Pzr Surge Pzr Spray Pzt Spray XI @ 640F @ 540F @ 640F XI @ 640F @ 540F @ 640F 0.00 80486.2 98462.27 100046.5 0.00 50250 78625 76125 0.10 56172.73 60419.55 63213.43 0.10 50250 60419.55 63213.43 J 0.20 38613.75 32945.43 36612.89 0.20 38613.75 32945.43 36612.89 l 0.30 27400.15 15399.76 19625.1 0.30 27400.15 15399.76 19625.1 ! 0.40 21927.22 6836.394 11334.03 0.40 21927.22 6836.394 11334.03 1 0.50 21394.72 6003.202 10527.33 0.50 21394.72 6003.202 10527.33 f 0.60 24806.82 11342.05 15696.42 0.60 24806.82 11342.05 15696.42 l 0.70 30972.16 20988.8 25036.44 0.70 30972.16 20988.8 25036.44 O.80 38503.77 32773.33 36446.26 0.80 38503.77 32773.33 36446.26 0.90 45819.14 44219.53 47528.51 0.90 45819.14 44219.53 47528.51 1.00 51140.2 52545.27 55589.52 1.00 50250 52545.27 55589.52 i Using the Third Order Curve Fit: CO 55266.6 83704.7 82032.4 l C1 -130231 -356694 -319250 S = SUM ( Ci
- Xi'i ), i = 0,1,2,3 C2 146351 497708 432426 C3 -18157.2 -169591 -136723 XI Res + Opr Stress w/ Cutoff, psi i 0.00 55266.6 83704.7 82032.4 l 0.05 49118.66 67093.07 67133.87 0.10 43688.85 52842.79 54294.94 0,15 38963.57 40326.66 43413.04 0.20 34929.18 30917.49 34385.66 0.25 31572.08 22988.09 27110.23 0.30 28878.65 16911.26 21484.22 0.35 26835.26 12559.82 17405.09 0.40 25428.3 9806.556 14770.29 i O.45 24644.15 8524.29 13477.28 l 0.50 24469.2 8585.825 13423.53 ;
0.55 24889.82 9863.967 14506.48 l 0.60 25892.4 12231.52 16623.59 0.65 27463.33 15561.3 19672.33 0.70 29588.97 19726.11 23550.15 0.75 32255.72 24598.75 28154.51 0.80 35449.95 30052.03 33382.86 0.85 39158.06 35958.76 39132.67 0.90 43366.41 42191.74 45301.39 0.95 48061.4 48623.79 51786.48 1.00 53229.4 55127.7 58485.4 Page 63
i l ' 32-1238965-00 l Axial Stress in Pressurizer Surge Nozzle , I 90000 80000 ", , --o-- Residual Stress i
- I Residual + l 70000 Operating l q l '. ,
l -60000 8 Res + Opr w/ l'
'b 125% Opr Temp
"( Yield Cutoff
' 'd 50000 ,
,r l
4' 3rd Order Curve Fit w' l p' \ - I l 40000 y 1, ,-
- l g 1 . ,
3 \ 's, , l a 30000 ' -- 5 b l \ U' j
\ " m o -o
\ I 10000
\
g
- l
/ l 0 * /
\\ /
-10000 /
a .if ,
'a ~"#
# l
-20000 !
l 0.00 0.25 0.50 0.75 1.00 Thru-Wall Position Figure A-1. Nonlinear Stress Distributions for the Pressurizer Surge Nozzle Safe End Page 64
32-1238965-00 Axial Stress in Pressurizer Spray Nozzle @ 540F 100000 o l
- + - Residual Stress 80000 d'N 0 - Residual + l
' Operating i l
q s Res + Opr w/ l 60000 h g ' 125% Opr Temp
\
Yield Cutoff , o
\
\ '
b 3rd Order Curve Fit , 40000 -\ '. p l
'j. ,
j t . , i \ . l
\ j ;
20000 \ n
\ . p' ;
b 'ti ,- /
\
' 1. *0 -E * ' /
O A- / '
/
\ /
N '
/
-20000 Ys
\ w c <, # #,n
-40000 0.00 0.25 0.50 0.75 1.00 Thru-Wall Position !
l i Figure A-2. Nonlinear Stress Distributions for the Pressurizer Spray Nozzle Safe End at 540F Page 65
32-1238965-00 l Axial Stress in Pressurizer Spray Nozzle @ 640F l 120000
--o-- Res! dual Stress D
- Residual +
Operating l 80000 n d " Res + Opr w/ t l , 125% Opr Temp
, Yield Cutoff 60000 'l g
3rd Order Curve Fit / l 1 \ b
~
40000 I( { ",-
= \ -
g en \ 20000 k ' "
\
t.,E=-o p" b -o* p/
\ p O /
g
-7(
\
/
o' t>
\ U
-20000 \ -
'A%oc^0
-40000 0.00 0.25 0.50 0.75 1.00 Thru-Wall Position Figure A-3. Nonlinear Stress Distributions for the Pressurizer Spray Nozzle Safe End at 640F Page 66
~ . _. .
B&W NUCLEAR TECHNOLOGIES 32-1238965-00 i A.2 Results and Conclusions ' Table A-3 shows the estimated remaining service life of pressurizer surge and spray non.le safe ends with i circumferential flaws. Dese results are graphically depicted in Figures A-4 through A-6. Table A-4 sontains the allowable flaw depths that can be justified for one fuel cycle (18 months) of continued operation. I I Use of the NUREG-0313 nonlinear residual axial stress distribution significantly increased the remaining life of l j j the re-evaluated components at 640 'F, especially the pressure spray nozzle safe end. His is readily apparent l i
; through a comparison of allowable 6:1 flaw depths for one fuel cycle from Tables 7 and A-4, as shown below.
Comparison of Allowable 6:1 Circumferential Flaw Depths for Different Assumed Stress Profiles j i Constant nrough-Wall Nonlinear Coyne "I'mpe Stress Stress Distribut,on i Pn Surge Nozzle Safe End 640 'F .085 in. .320 in. l Pr Spray Nozzle Safe End $40'F .205 in. .360 in. 1 I Pzr Spray Nozzle Safe End 640'F .015 in. .130 in. l j i j ! Table A-3. Summary of Time to Failure for Circumferential Flaws with an initial Depth of 0.010" l Note: Using NUREG-0313 nonlinear residual through-wall stress distribution plus constant i through-wall operating stress. Circumferential Flaw ID Component nick. Time to Failure (years) 1 (in.) 1/a=2 1/a=4 1/a=6 Jr b j 2 Pn Surge SE 1.005 40.00 40.00 40.00 3 Pn Spray SE @540*F 0.404 40.00 40.00 40.00 l 1 4 @640*F 0.404 40.00 10.64 5.36 i Table A-4. Summary of Allowable Circumferential Flaws for One Fuel Cycle (18 months) Note: Using NUREG-0313 nonlinear residual through-wall stress distribution plus constant i through-wall operating stress. j- Circumferential Flaw ID Component nick. Allowable Flaw Depth (in.) (in.) 1/a=2 1/a=4 1/a4 l 2 Pn Surge SE I.005 0.550 0.415 0.320 I l 3 Pr Spray SE @540*F 0.404 0.360 0.360 0.360 4 @640'F 0.404 0.240 0.180 0.130 I Date: 4/19/95 Prepared by: _D_f Killian Reviewed by: K.K. Yoon Date: 4/20/95 Page 67
32 1238965-00 Time to Failure vs. Initial Flaw Size 40 - : .
*: I. i
- I
; - . - . - 1/a = 2
. I 35 - ';
, i. tla=4
. g
....... tla = 6 i
. t 30 - 1
. 1, s
1
'. t 1 '
1 Qe 25 - '
\.
\ e
% : i.
E
- t. .
3 . t 20 - *.
. t o
'g i
' e . g b% 15 - *. 't
'. *1
; 1 to -
'. t.\.
=
s 5- '.
. N. .~ ,
'- 1
' ..........~~.~ ~. . . ....._
-*-*"**'"'~
0 . . . . . . . O O.1 0.2 0.3 0.4 0.5 0.6 0.7 Initial Flaw Size (inches) Figure A-4. Time to Failure for Pressurizer Surge Nozzle Safe End: Circumferential Semi-Elliptical inside Surface Flaws with NUREG-0313 Nonlinear Through-Wall Stress Distribution Page 68 l.
i l 32-1238965-00 Time to Failure vs. Initial Flaw Size l l 40 , t . . i . 1 i
',' . , g
- . - . - l/a = 2 l 35 - '..
1 l/a = 4 ' ! . l l t. i g
...... 1/a = 6
\ . . l t l 30 - '. t' l t.
- t. ,
. 1 i - . i
- 25 - .
e . t. 1 e .
>- t. ~ '.
t E '. '. : a '.
== 20 t. '
e
- u. '.
t, S e
'.'. 1
. t :
E 15 - p ., t,
. l
, . \. t,
. \
10 - ',
'g
. \.
\.
s 5- '. ., - s
'., N i
0 . , , . . . , O O.1 0.2 0.3 0.4 initial Flaw Size (inches) Figure A-5. Time to Failure for Pressurizer Spray Nozzle Safe End at 540F: Circumferential Semi-Elliptical inside Surface Flaws with NURFG-0313 Nonlinear Through-Wall Stress Distribution l ! Page 69
1 l 32-1238965-00 Time to Failure vs. Initial Flaw Size l 1 40 - - I
- - - - - 1/a = 2 1
35 - gj , ,4 l ...... 1/a = 6 1 30 - I. : l I
)
I 1 2 25 - i e e
>. I g i o
=e 20 - I. E ' l o
" I e
4 E i 15 - P ; I. I 10 - , *, j
\.
- \ :
5- .
\.s~~ ._ ~- ~. .
. 1
-=-= . _ , , ~ __ - - --
o , , , . O O.05 0.1 0.15 0.2 0.25 0.3 Initial Ficw Size (inches) Figure A-6. Time to Failure for Pressurizer Spray Nozzle Safe End at 640F: Circumferential Semi-Elliptical Inside Surface Flaws with NUREG-0313 Nonlinear Through-Wall Stress Distribution Page 70
32-1238965-00 A n = ndir B Verification of FORTRAN Programs This appendix contains calculations used to verify FORTRAN programs AX.F. CIRC.F and CINL.F. As a typical example, results will be verified for the Pressurizer Spray Nozzle Safe End at 640F. 1 Referenced output files (see Computer Output Microfict e)- i i (1) 4y_,ax.out (2) 4y_ circ.out (3) 4n_ circ.out i Geometry Data: Do= 4.500 in. Di= 3.692 in. Ro = 2.250 in. l Ri - 1.846 in. t= 0.404 in. l R= i 2.048 in. Rih = 4.56931 l-R/t - 5.06931 i a= 0.010 in. c= 0.030 in. (1/a = 6) , Material Data: Sy = 77.5 ksi(room temperature yield strength) i So = 60.9 ksi(operating temperature yield strength) Sf= 95.75 ksi(room temperature flow stress) n- 8.9 Applied Loads: Design pressure, pd = 2.500 ksi Equivalent axial yield load, Py = So pi (Ro^2-Ri^2) = 316.598 kip Faulted condition constant thru-wall stress, Sfc = 60.275 ksi Equivalent axial faulted condition load, Pfc = Sfc pi(Ro^2-Ri^2) = 313.349 kip ; 3rd Order Polynomial Through-Wall Stress Fits (ksi) l Nonlinear , _ Sy Operating S.'c
- SO 77.5 82.0324 60.275 St O -319.250 0 3 S2 0 432.426 0 i S3 0 -136.723 0 E.1 Axial, Semi-Elliptical Inside Surface Flaw with Constant Through-Wall Stress Field (AX.F) l E.1.1 Limit Load Spread- Program
sheet Output (1) l
= 1.00088 M =
[ l + (1.61c^2)/(R t) ]^0.5 , l t x = alt = 0.02475 ! po = Sf(t/Ro)[1-x]/[1-(x/M))
= 17.192 17.192 ksi {
l po/pd = 6.88 6.88 t i Page 71 t
__ _ . _ . _. - . . . . . _ _ _ __ . _ _ _ _ . _. __ _ = _ _ . _ - . . . _ _ _ _____ ___ i 32-1238 % 5-00 E.1.2 Stress Intensity Factor Solutions i Al A2 A3 A4 A5 A6 A7 m r $ 1.77670 -2.59750 2.75200 -1.32370 0.23630 1.06 0.28 0.58 0.41 0 ' 0.10450 0.41890 0.00000 0.00000 0.00000 0.25 0.20 0.22 0.26 l 0.07 0.16 0.10 0.06 i 2 0.02038 -0.00397 0.42126 0.00000 0.00000 0.07283 -0.36006 0.66883 0.00000 0.00000 0.085 0.02 0.05 0.00 3 f Stress Intensity Factor at Deepest Point i K1 = (pi*t)^.5
- SUM ( Si
- Gi), i=0,1,2,3 ]
Gi = A0 + (Al* alpha _i + A2* alpha _i^2 + A3* alpha _i^3 + A4* alpha _i^4 + A5' alpha _i^5) / F l i alpha _i = (a/t)/(a/c)^m I A0= 0 F = i 0.102(Ri/t)- 0.02 ]^0.05 = 0.96044 I ry - 1/(6 pi)*(n 1y(n+1)*(Kl(sySy)^2 Phi = 1/[l+{p/po)^2] i l se = a + phi *ry ry = 0.000352 phl= 0.979292 l a= 0.010 in. se = 0.010345 in. ; c= 0.030 in. c= 0.030 in. j Kl(s)- ksi*in^.5 Kl(ne)- ksi*in^.5 ; Spread- Spread- Program j i alpha (a) G(a) ~ sheet alpha (se) G(ae) sheet Output (l) ! 0.047482 0.082039 ! 0 0.046811 0.080956 l 0.03152 0.003863 0.032365 0.003978 j 2 0.027627 0.000592 0.028483 0.000611 3 0.02615 0.001739 0.027006 0.001788 7.07 7.16 l 7.16 l l I Stress Intensity Factor at Surface Point ) KI = (pi*t)^.5
- SUM ( Si
- Gsl), i=0,1,2,3 Gsi = Gi * [ A6 + A7(a/t)^2 ] * (a/c)^r KI(a)- ksi*in^.5 Kl(ae)- ksi*in^.5 Spread- Spread- Program i Gs(a) sheet Gs(ae) sheet Output (1) 0 0.054702 0.0562II 1 0.000726 0.000754 2 3.89E-05 4.02E-05 3 0.000148 0.000152 4.78 4.91 l 4.91 l Page 72 I
. , - __ - --- _. ,- , _ _ , . . , _ , . . _ , , . . - . . ~
32-1238 % 5-00 l E.1.3 Crack Growth for One Design Cycle Let: si = 0.0800 in. (initial crack depth) Kmax = 39.57 ksi*in^.5 f Kmin = 0.00 ksi*in^.5 Fatigue Cract: Growth for One Design Cycle da/dN = C*(dK)^n in/ cycle l t where C = 4.09E-10 j n = 3.349 I i and dN = 1 cycle dK = 39.57 ksi*in^.5 l Then: da/dN = 0.0001 in/ cycle ; da_ fatigue = 0.0001 in. Stress Corrosion Crack Growth for One Equivalent Design Cycle (1/12.5 years) i da/dt = D0*[Cl*(Kmax)^C2]^x in/sec with x = max { l.3539*(Kmax)%.ll ,1.0 ) where DO = $5.895 Cl = 3.386E-13 s C2 = 1.678 and dt = (1/12.5 yr) * (365 days /yr) * (24 hr/ day) * (3600 sec/hr)
= 2522880 sec. :
Then: x = 1.00000 } da/dt = 9.07E-09 in/sec j da_ SCC
= 0.0229 in. ;
1 Total Crack Growth l l da = da_ fatigue + da_ SCC = 0.0230 in. l l Spread. Program i sheet Output (1) J I New crack depth = al + da = 0.1030 l 0.1030 lin. Page 73
32-1238 % 5-00 E.2 Circumferential, Semi-Elliptical Inside Surface Flaw with Constant Through Wall Stress Field (CIRC.F) , E.2.1 Limit Load Spread- Program , sheet Output (2) 2 = t / Ro = 0.179556 .
= 0.012764 !
theta = (pic)/(4 Ri) x = a/t
= 0.024752 !
= 0.010077 Al = x [(1-zX2-2z+xz)+(1 z+xz)^21/(2[l+(2-z)(1-z)))
alpha = arc cos [Al' sin (theta)] . = 1.570668 ; Po = 2 pi R t Sf[2* alpha /pi-(x* theta / pix 2 2r+xzy(2-z)] = 497.69 497.69 kip Po/Py =
= 1.57 1.57 l l
E.2.2 Stress Intensity Factor at Deepest Point ! K! = (pi*t)^.5
- SUM ( Si ? (a/t)^i
- Gi ), 14),1,2,3 .
Gi = A1* alpha _i + A2* alpha _i^2 + A3* alpha _i^3 + A4* alpha _i^4 + AS* alpha _i^5
+ A6* alpha _i'(R/t-5) !
alpha _i = (a/t)/(a/c)^m l i Al A2 A3 A4 AS A6 m 0 1.8143 -1.9881 1.4382 -0.4680 0.0566 % 0.0067 0.50 , 1 1.0959 -0.9874 0.5399 -0.09303 0.0 0.0 0.38 l 2 1.1836 -2.3347 2.9756 -1.7652 0.39483 0.0 0.30 j 3 1.0029 -2.0160 2.5627 -1.4951 0.32759 0.0 0.25 l ry = 1/(6 pi)*(n-1)/(n+1)*(Kl(a)/Sy)^2 phi = 1/[1+(Py/Po)^2] se = a + phi *ry : l ry = 0.000296 I phl= 0.711908 l ! a= 0.010 in. se- 0.010211 in, c= 0.030 in. c=. 0.030 in. a/t = 0.024752 se / t = 0.025275 l Kl(s)- ksi*in^.5 Kl(ae)- ksi*in^.5 l Spread- Spread- Program l 1 alpha (s) G(a) sheet alpha (se) G(ne) sheet Output (2) ! 0 0.042873 0.074261 0.043322 0.075004 1 0.037577 0.039815 0.038067. 0.040316 2 0.034416 0.038088 0.034922 0.038611 3 0.032576 0.030618 0.03309 0.03107 6.48 6.55 l 6.55 l l l Page 74
,. - - . . _ - _ . . - - - . _ . . _ .- ._._ ___ _ , - _ - , _ . _ . . _ . ~ .
32-1238965-00 E.2.3 Crack Growth for One Design Cycle Let: ai = 0.0700 in. (initial crack depth) Kmax = 36.06 ksi*in^.5 Kmin = 0.00 ksi*in^.5 Fatigue Crack Growth for One Design Cycle da/dN = C*(dK)^n in/ cycle where C = 4.09E-10 n = 3.349 and dN = 1 cycle dK = 36.06 ksi*in^.5 Then: da/dN = 0.0001 in/ cycle da_ fatigue = 0.0001 in. Stress Corrosion Crack Growth for One Equivalent Design Cycle (1/12.5 years) da/dt = D0'[C1*(Kmax)^C2]^x in/sec i with x = max { l.3539'(Kmax)^-0.11,1.0 ) { where DO = 55.895 C1 = 3.386E-13 C2 = 1.678 , and dt = (1/12.5 yr) * (365 days /yr) * (24 hr/ day) * (3600 sec/hr)
= 2522880 sec.
l x = 1.00000 Then: l daldt = 7.76E-09 in/sec j da_ SCC
= 0.0196 in.
Total Crack Growth da = da_ fatigue + da_ SCC = 0.0196 in. Spread- Program sheet Output (2) New crack depth = ai + da = 0.08% l 0.08% lin. l 1 I Page 75 l I l
i 32 1238 % 5-00 E.3 Circumferential, Semi-Elliptical inside Surface Flaw with Nonlinear Thru-Wall Oper. Stresses (CINL.F) E.3.1 Limit Load ' Spmed- Program sheet Output (3) z = 1/ Ro
= 0.179556 ;
theta = (pic)/(4 Ri) = 0.012764 x = a/t
= 0.024752 :
= 0.010077 !
A1 = x [(1 z)(2-2z+xz)+(1 z+xz)^2]/{2[l+(2 zXI-z)l) I
= 1.370668 alpha = arc cos [Al' sin (theta)]
Po - 2 pi R t Sf[2* alpha /pi-(x* theta / pix 2-2r+xzy(2-z)]
= 497.69 497.69 kip i
= 1.59 -1.59 ,
Po/Pfc = , E.3.2 Stress intensity Factor at Deepest Point for Nonlinear 7hrough-Wall Operstmg Stress Distribution . i
~
K1 = (pi*t)^.5
- SUM ( Si * (a/t)^i
- Gi), i4,1,2,3 Gi = Al' alpha _i+ A2* alpha _i^2 + A3* alpha _i^3 + A4* alpha _i^4 + A5* alpha _i^5 l
+ A6* alpha _i'(R/t-5) .
alpha _i = (a/ty(a/c)^m i Al A2 A3 A4 A5 A6 m j 0 1.8143 -1.9881 1.4382 -0.4680 0.0566 % 0.0067 0.50 <
-0.04303 0.0 0.0 0.38 I 1 1.0959 -0.9874 0.5399 2 1.1836 -2.3347 2.9756 -1.~ td2 0.39483 0.0 0.30 - l 3 1.0029 -2.0160 2.5627 -1.4951 0.32759 0.0 0.25 ry = 1/(6 pi)*(n-ly(n+1)*(Kl(aySy)^2 phi = 1/[1+(Pfc/Po)^2] l ae = a + phi *ry ry = 0.0003
. phl= 0.716121 .
a= 0.010 in. se- 0.010215 in. l c= 0.030 in. c= 0.030 in. l a / t = 0.024752 se / t = 0.025284 Kl(a)- ksi*in^.5 Kl(ne)- ksi*in^.5 Spread- Spread- Program i alpha (s) G(a) sheet alpha (se) G(se) sheet Output (3) 0 0.042873 0.074261 0.04333 0.075017 1 0.037577 0.039815 0.038075 0.040325 2 0.034416 0.038088 0.034931 0.03862 3 0.032576 0.030618 0.033099 0.031077 6.52 6.58 l 6.58 l Page 76
32-1238 % 5-00 I E3.3 Stress Intensity Factor at Deepest Point for Constant Through-Wall Faulted Condition Stress K1 = (pi*t)^.5
- SUM ( Si * (a/t)^i
- Gi), i=0,1,2,3 !
Gi= A1* alpha _i+ A2* alpha _i^2 + A3* alpha _i^3 + A4* alpha _i^4 + A5' alpha _l^5 l
+ A6* alpha _i'(R/t-5) l alpha _i = (a/ty(a/c)^m I Al A2 A3 A4 A5 A6 m 0 1.8143 -1.9881 1.4382 -0.4680 0.056696 0.0067 0.50 -{
1 1.0959 -0.9874 - 0.5399 -0.09303 0.0 0.0 0.38 ; 2 1.1836 -2.3347 2.9756 -1.7652 039483 0.0 0.30 l 3 1.0029 -2.0160 2.5627 -1.4951 0.32759 - 0.0 0.25 . ry = 1/(6 pi)*(n-1y(n+1)*(Kl(a)/Sy)^2 l phi = 1/[l+(Pfc/Po)^2] 'l i ae = a + phi *ry ry = 0.000179 , phl= 0.716121 a= 0.010 in. se = 0.010128 in, c= 0.030 in. c= 0.030 in, a / t = 0.024752 se / t = 0.02507 Kl(a)- ksi*in^.5 Kl(se)- ksi*in^.5 f Spread. Spread- Program sheet Output (3) I i alpha (s) G(a) sheet alpha (ae) G(ae) O 0.042873 0.074261 0.043147 0.074714 l 1 0.037577 0.039815 0.037876 0.04012 l 2 0.034416 0.038088 0.034724 0.038406 l 3 0.032576 0.030618 0.032889 0.030893 . ! 5.04 5.07 l 5.07 l i l Pa8e 77
l 32 1238 % 5-00 E.3.3 Crack Growth for One Design Cycle I Let: si = 0.2800 in. (initial crack depth) -
. Kmax ' = 31.% ksi*in^.5 Kmin = 0.00 ' ksi*in^.5
)
Fatigue Crack Growth for One Design Cycle i da/dN = C*(dK)^n in/ cycle , I where C = 4.09E-10 n = 3349 , and dN = 1 cycle ; dK = 31.% ksi*in^.5 i Then: da/dN = 0.00004 in/ cycle l da_ fatigue = 0.00004 in. [ i Stress Corrosion Crack Growth for One Equivalent Design Cycle (1/12.5 years) l t da/dt = D0'[C1*(Kmax)^C2]^x in/sec i with x = max { l.3539*(Kmax)^.0.11,1.0 ) where D0 = 55.895 C1 = 3.386E C2 = 1.678 , i and dt = (1/12.5 yr) * (365 days /yr) * (24 hr/ day) * (3600 sec/hr)
= 2522880 sec. l i
i
= 1.00000 ;
j Then: x daldt = 6.34E-09 in/sec ! ( ! da SCC = 0.0160 in. l Total Crack Growth
. s l
- da = da_ fatigue + da_ SCC = 0.0160 in. .
l Spread- Program sheet Output (3) New crack depth = ai + da = 0.2960 l 0.2960 lin. l Page 78
. -- - - - . - , . . -- . - . .-. ~ . - . . - - -- . - . . - - - .-
J P B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 l
- t I
Anoendix C Computer input Files File DHMiaa ,
?
geometry.inp Outside and inside diameters for each nonle, j ax_cof.inp Influence coefficients for an axial flaw.~ l l 3 cire_cof.inp influence coefficients for a circumferential flaw. j I
#y.inp Miscellaneous input for noale ID "#" for use with programs AX.F and CIRC.F for constant through-wall stresses (#=1,2,3,..14). l l
i
#n.inp Miscellaneous input for noale ID "#" for use with program CINL.F for NUREG-0313 nonlinear through-wall stress l distributions (#=2,3,4).
File geometry.inp i 00 ID l 4 1 1.315 0.815 t 2 12.750 10.740 3 4.500 3.692 4 4.500 3.692 5 13.000 10.741 i 6 12.750 10.741 7 2.375 1.689 l 8 1.250 0.625 I 9 1.250 0.377 10 13.000 10.741 i 11 3.500 2.693 12 2.375 1.689 1 13 1.250 0.625 14 1.250 0.377 File ax_cof.inp $ 6 6 A A A A A A a r . 0.0 1.7767 -2.5975 2.7520 -1.3237 0.2363 1.06 0.28 0.58 0.41 0.0 0.1045 0.4189 0.0 0.0 0.0 0.25 0.20 0.22 0.26 0.0 0.02038 -0.00397 0.42126 0.0 0.0 0.07 0.16 0.10 0.06 ! 0.0 0.07283 -0.36006 0.66883 0.0 0.0 0.085 0.02 0.05 0.0 File circ _cof.inp A 6' A A A A a 1.8143 -1.9881 1.4382 -0.4680 0.056696 0.0067 0.50 1.0959 -0.9874 0.5399 -0.09303 0.0 0.0 0.38 1.1836 -2.3347 2.9756 -1.7652 0.39483 0.0 0.30 1.0029 -2.0160 2.5627 -1.4951 0.32759 0.0 0.25 Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Dae: ' 4/20/95 Page 79
B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 File ly.inp. 4.09E-10 ! Paris Law scaling constant 3.349 ! Paris Law slope constant 310.18 ! Kic 46.2 36.3 i RT & oper temp yield stress 72.2 ! RT flow stress 8.9 ! strain hardening coefficient 1 ! number of fatigue groups 1 500 1 fatigue group no. & cycles 0.0 0.25 0.50 0.75 1.00 i z/t locations 46.2 46.2 46.2 46.2 46.2 I operating stresses 46.2 46.2 46.2 46.2 46.2 i SCC stresses 55.895 i SCC coefficient at 640F j I File 2y.inp l 4.09E-10 i Paris Law scaling constant I 3.349 ! Paris Law slope constant : 310.18 I Kic 51.2 40.2 ! RT & oper temp yield stress j 75.75 ! RT flow stress J 8.9 i strain hardening coefficient l 1 ! number of fatigue groups 1 500 i fatigue group no. & cycles 0.0 0.25 0.50 0.75 1.00 ! z/t locations 51.2 51.2 51.2 51.2 51.2 ! operating stresses 51.2 51.2 51.2 51.2 51.2 ! SCC stresses 55.895 i SCC coefficient at 640F File 3y.inp 4.09E-10 1 Paris Law scaling constant ! 3.349 ! Paris Law slope constant . 310.18 ! Kic l 77.5 62.9 ! RT & oper temp yield stress ; 95.75 ! RT flow stress 8.9 ! strain hardening coefficient 1 ! number of fatigue groups 1 500 l fatigue group no. & cycles 0.0 0.25 0.50 0.75 1.00 1 z/t locations t 77.5 77.5 77.5 77.5 77.5 ! operating stresses 77.5 77.5 77.5 77.5 77.5 ! SCC stresses 3.687 ! SCC coefficient at 540F Fi'ie 4y.inp 4.09E-10 ! Paris Law scaling constant 3.349 ! Paris Law slope constant 310.18 ! Kic 77.5 60.9 ! RT & oper temp yield stress 95.75 ! RT flow stress 8.9 I strain hardening coefficient 1 ! number of fatigue groups 1 500 ! fatigue group no. & cycles 0.0 0.25 0.50 0.75 1.00 1 z/t locations 77.5 77.5 77.5 77.5 77.5 ! operating stresses 77.5 77.5 77.5 77 5 77.5 i SCC stresses 55.895 i SCC coefficient at 640F Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 80
B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 i File Sy.inp t
'4.09E-10 ! Paris Law scaling constant :
3.349 ! Paris Law slope constant ! 306.28 ! Kic 51.2 41.0 ! RT & oper temp yield stress ( 75.75 ! RT flow stress , 8.9 ! strain hardening coefficient ; 1 ! number of fatigue groups j 1 500 !fatiguegroupno.& cycles 0.0 0.25 0.50 0.75 1.00 ! z/t ocations 51.2 51.2 51.2 51.2 51.2 ! operating stresses 51.2 51.2 51.2 51.2 51.2 ! SCC stresses 15.316 ! SCC coefficient at 590F File 6y.inp
! Paris Law scaling constant I 4.09E-10 3.349 ! Paris Law slope constant
! Kic 306.28 ,
51.2 41.0 ! RT & oper temp yield stress 75.75 ! RT flow stress 8.9 ! strain hardening coefficient 1 ! number of fatigue groups 1 500 i fatigue group no. & cycles : 0.0 0.25 0.50 0.75 1.00 1 z/t locations , 51.2 51.2 51.2 51.2 51.2 ! operating stresses 51.2 51.2 51.2 51.2 51.2 ! SCC stresses 15.316 ! SCC coefficient at 590F File 7y.inp ; l 4.09E-10 ! Paris Law scaling constant ! ! 3.349 ! Paris Law slope constant r ! 306.28 ! Kic 37.1 29.7 ! RT & oper temp yield stress 65.15 ! RT flow stress . 0.9 ! strain hardening coefficient ! 1 ! number of fatigue groups i l ? fatigue group no. & cycles i 1 500 l 0.0 0.25 0.50 0.75 1.00 ! z/t locations 1 37.1 37.1 37.1 37.1 37.1 ! operating stresses 37.1 37.1 37.1 37.1 37.1 ! SCC stresses 15.316 ! SCC coefficient at 590F l File By.inp 4.09E-10 ! Paris Law scaling constant 3.349 ! Paris Law slope constant 306.28 ! Kic 39.8 31.8 ! RT & oper temp yield stress 67.25 ! RT flow stress 8.9 ! strain hardening coefficient 1 ! number of fatigue groups 1 500 ! fatigue group no. & cycles 0.0 0.25 0.50 0.75 1.00 ! z/t locations 39.8 39.8 39.8 39.8 39.8 ! operating stresses 39.8 39.8 39.8 39.8 39.8 ! SCC stresses 15.316 ! SCC coefficient at 590F Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 81
-.. .~ - - _. . . . - -. - . - - - . - -
b B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 1 i File 9y.inp l 4.09E-10 ! Paris Law scaling constant i 3.349 ! Paris Law slope constant i 306.28 ! Kic 48.0 38.4 ! RT & oper temp yield stress. 73.5 i RT flow stress
- 8.9 ! strain hardening coefficient 3 1 I number of fatigue groups l 1 500 i fatigue group no. & cycles l 0.0 0.25 0.50 0.75 1.00 1 z/t locations j 48.0 48.0 48.0 48.0 48.0 ! operating stresses i I
48.0 48.0 48.0 48.0 48.0 i SCC stresses i l 15.316 ! SCC coefficient at 590F e File 10y.inp 4.09E-10 ! Paris Law scaling constant i 3.349 ! Paris Law slope constant ] 306.28 I Kic ;
. 51.2 41.5 ! RT & oper temp yield stress :
} 75.75 l RT flow stress >
- 8.9 ! strain hardening coefficient ,
j 1 ! number of fatigue groups- l i 1 500 ? fatigue group no. & cycles i 0.0 0.25 0.50 0.75 1.00 ! z/t locations ; j 51.2 51.2 51.2 51.2 51.2 ! operating stresses , 51.2 51.2 51.2 51.2 51.2 ! SCC stresses , j 3.687 ! SCC coefficient at 540F l 3 i File 11y.inp ) 4.09E-10 ! Paris Law scaling constant-a 3.349 ! Paris Law slope constant ;
- 302.33 ! Kic
! 37.1 30.1 ! RT & oper temp yield stress l
- 65.15 ! RT flow stress
! 8.9 i strain hardening coefficient I
- 1 ! number of fatigue groups l
- 1 500 l fatigue group no. & cycles i j 0.0 0.25 0.50 0.75 1.00 ! z/t locations j 37.1 37.1 37.1 37.1 37.1 ! operating stresses 1 37.1 37.1 37.1 37.1 37.1 ! SCC stresses 3.687 ! SCC coefficient at 540F l
i j File 12y.inp 4.09E-10 ! Paris Law scaling constant i 3.349 ! Paris Law slope constant j 302.33 i Kic 1 37.1 30.1 ! RT & oper temp yield stress J 65.15 ! RT flow stress
- 8.9 ! strain hardening coefficient i
! 1 I number of fatigue groups )
1 500 1 fatigue group no. & cycles - i 0.0 0.25 0.50 0.75 1.00 ! z/t locations 4 37.1 37.1 37.1 37.1 37.1 l operating stresses l i 37.1 37.1 37.1 37.1 37.1 ! SCC stresses ; 3.687 ! SCC coefficient at 540F { , Prepared by: D.E. Killian Date: 4/19/95 j Reviewed by: K.K. Yoon Date: 4/20/95 Page 82 l l
B&W NUCLEAR TECHNOLOGIES 32-1238965-00 File 13y.inp 4.09E-10 ! Paris Law scaling constant 3.349 ! Paris Law slope constant 303.33 ! Kic 39.8 32.3 ! RT & oper temp yield stress 67.25 ! RT flow stress 8.9 ! strain hardening coefficient 1 ! number of fatigue groups 1 500 . I fatigue group no. & cycles 0.0 0.25 0.50 0.75 1.00 ! z/t locations 39.8 39.8 39.8 39.8 39.8, ! operating stresses 39.8 39.8 39.8 39.8 39.8 ! SCC stresses 3.687 ! SCC coefficient at 540F l l File 14y.inp ! 4.09E-10 ! Paris Law scaling constant 3.349 ! Paris Law slope constant 302.33 ! Kic 48.0 38.9 ! RT & oper temp yield stress 73.5 ! RT flow stress 8.9 ! strain hardening coefficient 1 ! number of fatigue groups 1 500 ! fatigue group no. & cycles 0.0 0.25 0.50 0.75 1.00 ! z/t locations 48.0 48.0 48.0 48.0 48.0 ! operating stresses 48.0 48.0 48.0 48.0 48.0 1 SCC stresses 3.687 ! SCC coefficient at 540F File 2n.inp 12.750 10.740 ! OD & 10 4.09E-10 3.349 ! da/dN constants: C & n 310.18 ! Kic 51.2 40.2 ! RT & oper temp yield stress 75.75 ! RT flow stress 8.9 ! strain hardening coefficient 55.895 ! SCC coefficient at 640F 1 ! number of fatigue loads i 1 500 ! fatigue load no. & cycles l 48.768 ! faulted condition stress 0.00. 50250. ! x/t position 0 10 50250. ! vs.
- 0. 2 .. 38613.75 ! residual + operating stress 0.30 27400.15 0.40, 21927.22 0.50, 21394.72 0.60. 24806.82 0.70. 30972.16 i
0.80. 38503.77 0.90. 45819.14 1.00. 50250. Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 83
l l 1 B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 j File 3n.inp 4.500 3.692 ! OD & ID i 4.09E-10 3.349 ! da/dN constants: C&n ! 310.18 ! Kic > 77.5 62.9 I RT & oper temp yield stress 95.75 ! RT flow stress 8.9 ! strain hardening coefficient i 3.687 ! SCC coefficient at 540F 1
! number of fatigue loads l 1 500 ! fatigue load no. & cycles 56.691 ! faulted condition stress !
0.00. 78625. ! x/t position 0.10. 60419.55 ! vs. j 0.20, 32945.43 ! residual + operating stress 0.30. 15399.76 - 0.40, 6836.394 i 0.50. 6003.202 I 0.60. 11342.05 ! 0.70, 20988.8 0.80. 32773.33 0.90. 44219.53 l 1.00. 52545.27 l File 4n.inp l 4.500 3.692 ! OD & ID : l 4.09E-10 3.349 ! da/dN constants: C&n i I 310.18 I Kic 77.5 60.9 ! RT & oper temp yield stress l 95.75 ! RT flow stress ; i 8.9 ! strain hardening coefficient i 55.895 ! SCC coefficient at 640F 1 ! number of fatigue loads 1 500 ! fatigue load no. & cycles 60.275 ! faulted condition stress i 0.00, 76125. ! x/t position 0.10, 63213.43 ! vs. 0.20. 36612.89 ! residual + operating stress 0.30, 19625.1 0.40. 11334.03 0.50 10527.33 0.60. 15696.42 0.70. 25036.44 0.80. 36446.26 0.90. 47528.51 1.00. 55589.52 , 1 l l l l ! l l l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 84 , I l
._ . . ._. _ _ _ __ _ _ __ _ _ __ _. _ _ = _ _._ _ . - _ _
i B&W NUCLEAR TECHNOLOGIES 32-1238 % 5-00 l c 6 Anoendix D List of Computer Output Microfiche l !
. Ihe computer output microfiche listed below are contained in Reference 15.
File Description Dg.g l Output file with time to failure data from program AX.F for all nozzles. 3/22/95 fail _ax.out -l Output file with time to failure data from program CIRC.F for all nozzles. 3/23/95 j fail _ circ.out i Output file with time to failure data from program CINLF for nozzle 3/23/95 - , fail _cint.out ID #'s 2,3 and 4. ; Output file with summary of crack growth results from program 3/22/95' sum _ax.out AX.F for all nozzles. , Output file with summary of crack growth results from program 3/23/95 sum _ circ. cut CIRC.F for all nozzles. y Output file with summary of crack growth results from program 3/23/95 : sum _cint.out CINL.F for nozzle ID #'s 2,3 and 4. ,
#y u.out Output files with detailed crack growth results from program 3/22/95 ;
AX.F for nozzle ID "#" (#=1,2,3,..14). [
#y_ circ.out Output files with detailed crack growth results from program' 3/23/95 ;
CIRC.F for nozzle ID "#" (#-1,2,3,...,14). _
#n_ circ.out Output files with detailed crack growth results from program 3/23/95 'i CINL.F for nozzle ID "#" (#=2,3,4). ,
l l l Prepared by: D.E. Killian Date: 4/19/95 Reviewed by: K.K. Yoon Date: 4/20/95 Page 85
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