ML050980195
| ML050980195 | |
| Person / Time | |
|---|---|
| Site: | Hope Creek  |
| Issue date: | 04/02/2005 |
| From: | Coward R, Heinz M, Hibbard J MPR Associates |
| To: | Office of Nuclear Reactor Regulation, Public Service Enterprise Group |
| References | |
| Task No. 1108-0502-0002-00 1108-0002-08 | |
| Download: ML050980195 (15) | |
Text
MPR Associates, Inc.
WMPR 320 King Street Alexandria, VA 22314 CALCULATION TITLE PAGE Client:
PSEG Nuclear LLC Page 1 of 15 Project: Task No.
Hope Creek Decontamination Port 1 108-0502-0002-00
Title:
Calculation No.
Fatigue Crack Growth Evaluation 1 108-0002-08 Preparer / Date Checker / Date Reviewer & Approver Date Rev. No.
2-o5 0 J. L. Hibbard M. Heinz R. Coward QUALITY ASSURANCE DOCUMENT This document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurance requirements of IOCFR50 Appendix B, as specified in the MPR Quality Assurance Manual.
MPR-OA Form OA-3.1 -1. Rev. 1
MPR Associates, Inc.
- AMPR 320 King Street Alexandria, VA 22314 RECORD OF REVISIONS Calculation No. Prepared By Checked By Page: 2 1108-0002-08 A ".LcA}44L Revision I Affected Pages Description 0 All Initial Issue Note: The revision number found on each individual page of the calculation carries the revision level of the calculation in effect at the time that page was last revised.
MPR Associates, Inc.
HIFM P D320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 3 1108-0002-08 (LRevision: A 0 Table of Contents 1.0 Purpose .................................... 4 2.0 Summary .................................... 4 3.0 Approach ..................................... 6 4.0 Calculation ....................................
4.1 Data ...................................... 8 4.2 Acceleration for Fatigue Crack Initiation ..................................... 10 4.3 Minimum Acceleration for Crack Growth ..................................... 11 4.4 Crack Growth Functions ..................................... 12 4.5 Crack Growth Calculation ..................................... 14 5.0 References ................................... 15 MPR QA Form: OA-3.1-3. Rev. 0
Calculation No.:
,AMPR Prepared By: 3 1108-0002-08 MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 CheckedBy:
Chce1y A A.9 PageNo.: 4 aeN.
1.0 PURPOSE The two purposes of this calculation are:
- Determine the acceleration that could cause a fatigue crack to initiate. Three cases are considered corresponding to the three design endurance limit stresses from the ASME Code (ASME Code Curves A, B, and C for different mean stress conditions).
- Determine the approximate number of cycles to propagate a crack through the wall thickness of the pipe. The three cases considered are for pipe accelerations that correspond to the results for crack initiation as discussed in the previous bullet.
2.0
SUMMARY
The acceleration that produces an alternating stress equal to the design value from the ASMEE Code at 101 l cycles is provided in the following table. The table provides the acceleration for crack initiation for the three fatigue design curves in the ASME Code (labeled A through C).
"ASME" "EnduranceLimitAlternatingStress" "Acceleration" "Curve" okra" f TI= "A" 23.8 0.72 "B" 165 0.5 "C" 13.7 0.41 The minimum acceleration that gives a stress intensity factor at the crack tip greater than the threshold stress intensity factor for crack growth at the pipe OD is amin = 0.29 g. This is based on a threshold stress intensity factor for crack growth assumed to be AKmin = S ksi If; and a defect initial depth of ad 1 =0.021 in. The defect size is based on the metalographic examination.
The crack growth rate at the threshold stress intensity factor for crack growth is
-8 in dadnmin = 3.73 x 10 -n-. At a frequency of fA' = 123 Hz , this crack growth rate will go through the cycle pipe wall thickness in tmax = 0.85 day.
_ _*Calculation No.:
WI YM Prepared By: )LY 9- 1108-0002-08 MPR Associates, Inc. , Revision No.: 0 320 King Street CheckedJBy: Ji1 . PageNo.: 5 Alexandria VA 22314 ChckdBy ag o.
The number of cycles to propagate a crack through the pipe wall (defined as 70% though the pipe wall) is provided in Table T2 below for each of the accelerations in Table Ti above. The approximate time for the crack to propagate through the pipe wall is based on a frequency of fn =123 Hz These are approximate results based on a simplified model for the crack growth. The results show the crack grows through the pipe wall in less than one day. This is consistent with the maximum time to grow the crack through the pipe wall discussed on the previous page.
"Acceleration" "Cyclesfor" "ApproximateTime' Vg" "Through-wallCrack" "hr" 72= 0.72 170000 0.4 0.5 550000 1.3 0.41 1.02x 106 23
Calculation No.:
WM P R Prepared By: D U EL 1108-0002-08 MPR Associates, Inc. Revision No.: 0 320 King Street Checked By: o PageNo.: 6 Alexandria VA 22314ChceByPaeN:6 3.0 APPROACH This calculation is a simplified fatigue crack growth calculation. The actual defect location is a subsurface elliptical flaw in the circumferential direction as described in Reference 2. The defect is near the pipe OD, so that after some initial crack growth, the defect becomes a surface defect similar to that shown in Figure 1.
Figure 1. Approximate Crack Configuration after Defect Grows to Pipe OD The growth of the defect from cyclic loads is predicted using the Paris equation.
-a= CI-AIK1 diV da where d = defect growth per cycle diV AK, = cyclic range of stress intensity factor C1, n = crack growth constants
Calculation No.:
M
. PRPrepared By: U 1108-0002-08 MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: " .1~ Page No.: 7 The cyclic range of stress intensity factor is calculated with the following equation:
AKl = M-Aa where ha effective stress range M magnification factor a crack depth The magnification factor is based on an edge crack in a semi-infinite plate. The crack configuration for the magnification factor is shown in Figure 2. The magnification factor is a constant that does not change with crack depth. This model for the crack in the pipe is approximate. At small crack depths, the flat plate model will give good results, but at larger crack depths the magnification factor will vary.
The approach used in this calculation is sufficient for evaluating the propagation of shallow cracks as well as showing the crack propagation occurs in a short time as discussed in Section 2.0.
Figure 2. Model for Crack Magnification Factor Section 4.1 below shows that stress varies significantly through the thickness of the pipe. The maximum stress occurs at the pipe OD and the minimum occurs at the pipe ID. The stress used to grow the crack at each cycle is the stress range at the crack depth.
The initial defect size is based on the metalographic examination. The defect that was identified was a sub-surface elliptical defect with minor radius of a,., =0.021 in. For this calculation, it was assumed that a defect with this depth is at the surface. It is noted that this initial defect size is one-half the size of the sub-surface defect. Using this initial defect overestimates the number of cycles for the crack to grow through the pipe wall.
Calculation No.:
MIM PR Prepared By: , : 1108-0002-08 MPR Associates, Inc. Revision No.: 0 AlexandriaVA22314 Checked By: ,AA. + Page No.: 8 4.0 CALCULATION 4.1 Data Top:= 550-F approximate operating temperature; assumption twt .- a337.in pipe wall thickness; assumption 0.042 . defect initial depth; scaled from Ref. 2, Figure 8 ao .- ,n A := 123 11z frequency for approximate conversion of cycles into time Ehot.30tSS := 25.55-106psi modulus of elasticity of 304 SS at the operating temperature, Ref. 4, Table 1-6.0 Fatigue Crack Growth Equations (Reference 3, C-8410; austenitic stainless steel in air) crack growth exponent; Ref. 3, C-8410 fl3O4SS := 3.3 S := I scaling parameter; based on R=-1 and Ref. 3, C-8410
- T 0P -6 (T 01 9 3r
-10.009+8.12.10 4-1.13 +1.02-10 -
F F F . in 30J4'y'- v (ksiNi;n)n C304SS = 1.84 x 10 in temperature corrected proportionality constant for crack (ksi-NFn)f34SS growth; Ref. 3, C-8410 M := 1.1215 magnification factor for an edge crack in a semi-infinite plate; Ref. 5, p. 8.la
,gmin := 5-ksi-,fin approximate minimum stress intensity factor threshold for crack growth; assumption; see Ref. 3, Figure C-8410-1 Fatigue Crack Initiation Data (23.8 (A" ASME Code alternating stress at 101I cycles from design Sa = 16.5 jksi c := "B" fatigue curve for austenitic stainless steel; Ref. 4, Figure K13.7) §tC 1-9.2.2 Efaigue := 28.3-10 *psi modulus of elasticity for fatigue data; Ref. 4, Figure 1-9.2.2
_Ilr~r No.:
IMMPR MPR Associates, Inc.
Prepared By: 4
^Calculation 1108-0002-08 Revision No.: 0 320 King Street Checked By: Ha - PageNo.: 9 Alexandria VA 22314 ChceIy aeN.
Stress and Stress Distribution Function Slmax:= 29.967.- maximum axial stress at pipe OD for reference case with 1 g g acceleration; Ref. 1 ksi S3min : S=max S3mitz = -29.97 minimum axial stress at pipe OD for reference case with 1 g acceleration; Ref. 1 SI (SWmax - S3min) SI = 59.93 - stress range at pipe OD 8
Define a function for the stress range distribution through the pipe wall. The stress range is twice the alternating stress from Reference 1. Data for the stress vs. distance from the pipe OD are in Reference
- 1. The stress distribution is based on a Ig pipe acceleration.
' 0.337 29.967 0.2528 18.016 ksi t:= two - 0.1685 *in a:= 13.106 0.0842 8.7483 0 3.6388 zla(x) = 2-linterp(l, a7x) 60 to Notes:
-:2 48 The depth dimension in figure is based on the
- a distance from the pipe OD.
4t: 36 Ln If 24 The effective stress range is twice the alternating stress.
t 12 The stress profile from Reference 1 varies 14`47 significantly through the pipe wall. The reason 0 0.4 for the variation is the close proximity of the weld 0 a0 0.2 0.3 Radial Distancefrom OD (in) to the weldolet. Further away from the weldolet in the axial direction, there is little variation is Pipe Pipe stress through the wall thickness, which is the OD ID expected result for a pipe with an applied bending moment.
Calculation No.:
A M PR Prepared By: \ G 1108-0002-08 MPR Associates, Inc. Revision No.: 0 320 King Street C B Alexandria VA 22314 Checked By: A. Page No.: 10 4.2 Acceleration for Fatigue Crack Initiation Calculate the acceleration for fatigue crack initiation. No stress concentration factor is required in this calculation since the finite element results in Reference 1 captured the effects of stress concentration.
SaE(Ehoi304SS)
sani Efatigil ainil:= SIn=r a0.72'
an = IO.Sl g 1..41)
,A MP m R Calculation No.:
W^hiPR Prepared By: 1108-0002-08 MPR Associates, Inc. Revision No.: 0 320 King Street V21Checked By: At.i Page No.: 11 Alexandria VA 22314 CekdB:~Pg o:1 4.3 Minimum Acceleration for Crack Growth Calculate the minimum acceleration that gives a stress intensity factor at the crack greater than the threshold stress intensity factor for crack growth.
amin := aguess - 1*g a
l root(Amin - aguess.M .Sl.1J;r. aguess) amin = O.29g The crack growth rate at the threshold stress intensity factor for crack growth is:
3 dadnmin := S C3 04SS AKmin SS dadnrnin = 3.73 x 10 -
cycle The maximum time to grow the crack through the pipe wall at the minimum crack growth rate is (frequency of fn =123 Hz ):
twt lmax:=
dadnmin-fn imax = 0.85 day
§0 M PR PR Prepe BCalculation Prepared By: 3 (L1'L JLX No.:
1108-0002-08 MPR Associates, Inc. Revision No.: 0 320 King Street CheckedBy: S QuaAe 1 Alexandria VA 22314 CeedB:Page No.: 12 4.4 Crack Growth Functions The crack growth for an application of a single cycle is:
a&(a,SI) := AK - M-SIW-Ir dadn v- S.C304SSAK if AK > Amin O-in otherwise A function for calculating crack growth for multiple applications of a single transient is provided below.
The parameters passed to the function are as follows:
a = initial crack depth t = component thickness acc = accuracy criterion (see discussion below) accel = acceleration to apply to 1 g stress distribution At the start of the crack growth calculation, the membrane stress, bending stress, and magnification factors are updated after each transient, i.e., N=1. As the calculation progresses, N is increased to reduce the calculation time provided the accuracy criterion is met and N is less than the total cycles divided by 10. The accuracy criterion "min" is the total projected crack growth in the transient at the current value of N divided by the initial flaw size.
The accuracy criterion used is:
acc:= 0.01%
The number of cycles per iteration, N, is allowed to increase if the total crack growth in the transient is projected to be less than acc =0.01 % of the initial crack size. Using values smaller than acc =0.01 % did not significantly change the answer.
Calculation No.:
MOM PR MPR Associates, Inc.
Prepared By: 35 1108-0002-08 Revision No.: 0 320 Kingdreet Checked By: AStr Alexandria VA 22314 CheckdABy:Page No.: 13 through 70% of the The following function determines the number of cycles for the crack to propagate The following function determines the number of cycles for the crack to propagate through 70% of the wall thickness. For the purpose of this calculation, this is considered a through-wall crack.
aend:= 70.%
Crkj(a,t,acc,accel) := count - 1 test v- 1 N v I while test a v accel.Ao(a) ao ld +- a a v- afdr + N.a,(a, a) a - aold N*- 2-N ~f _ac aold test v- 0 if a > aend-t v count >10 count +- count + N count
Calculation No.:
M PR EMPR Associates, Prepared By: S Liz 1108-0002-08 Inc. Revision No.: 0 Alexandria VA 22314 Checked By: A Page No.: 14 4.5 Crack Growth Calculations Calculate the number of cycles to grow the crack through the wall thickness of the pipe for the accelerations calculated in Section 4.2.
ncy := Crk,(ao.,twvacc,iaina)
The approximate time to accumulate this number of cycles at a frequency of f, = 123 Hz is:
ncyc t :=
An
=1.25 hr 231
F M 7Pj- &1 PPACalculation R R Prepared By: J 1108-0002-08 No.:
MPR Associates, Inc. . Revision No.: 0 AlexandriaVA22314 Checked By: I. Page No.: 15
5.0 REFERENCES
- 1. MPR Calculation No. Attachment 17 to C-0142, "Harmonic Stress Analysis of Loop 'B' Port,"
Revision 0.
- 2. Hope Creek "B" Loop Decontamination Port Cracking Preliminary Results, attachment to e-mail from A. Roberts (PSE&G) to R. Keating (MPR), 4-1-05,
Subject:
Areva Report.
- 3. 2004 ASME B&PV Code,Section XI.
- 5. Hiroshi Tada, "The Stress Analysis of Cracks Handbook, Second Edition," Paris Productions Incorporated, St. Louis, MO, 1985.