ML13316A524
| ML13316A524 | |
| Person / Time | |
|---|---|
| Site: | San Onofre  |
| Issue date: | 10/31/1980 |
| From: | Chirigos J, Kaiser W, Swamy S WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML13316A523 | List: |
| References | |
| TAC-44652, WCAP-9808, NUDOCS 8101160476 | |
| Download: ML13316A524 (31) | |
Text
WESTINGHOUSE CLASS 3 Co CUSTOMER-DESIGNATED DISTRIBUTION 00~
FATIGUE CRACK GROWTH EVALUATION FOR SAN ONOFRE UNIT 1 MAIN STEAM LINE PIPE By S. A. Swamy W. T. Kaiser October, 1980 PREPARED BY WESTINGHOUSE FOR SOUTHERN CALIFORNIA EDISON COMPANY APPROVED:
J. N. Chirigos, Manager Structural Materials Engineering Work Performed Under SCFN-2020 Although the information contained in this report is nonproprietary, no distribution shall be made outside Westinghouse or its Licensees without the customer's approval.
WESTINGHOUSE ELECTRIC CORPORATION Nuclear Energy Systems P.O. Box 355 Pittsburgh, Pennsylvania 15230 8 0 118011
PREFACE This report has been technically reviewed and the calculations checked.
W. T. Kaiser 01
ABSTRACT A fatigue crack growth evaluation for the San Onofre Unit 1 main steam line pipe is presented in this report. The analysis is based on postulated initial flaws of 0.125, 0.250 and 0.375 inch depths. The postulated flaws are oriented in the circumferential direction. The fatigue crack growth analysis has been conducted in the same manner as suggested by Section XI, Appendix A of the ASME Boiler and Pressure Vessel Code.
v
TABLE OF CONTENTS SECTION TITLE PAGE 1
INTRODUCTION 1-1 2
THERMAL AND STRESS ANALYSIS 2-1 2-1 Assumptions 2-1 2-2 Thermal Analysis - Temperatures and Stresses 2-1 2-3 Mechanical Stress Analysis 2-3 3
DESIGN TRANSIENTS 3-1 4
STRESS INTENSITY FACTOR CALCULATIONS 4-1 4-1 KI Expression 4-1 5
FATIGUE CRACK GROWTH RATE 5-1 5-1 ASME Section XI Crack Growth Law for 5-1 Water Reactor Environment 6
FATIGUE EVALUATION 6-1 7
RESULTS AND CONCLUSIONS 7-1 8
REFERENCES 8-1 Vii
LIST OF ILLUSTRATIONS FIGURE TITLE PAGE 2-1 San Onofre Unit 1 Main Steam Line 2-2 4-1 Linearized Representation of Stresses 4-2 4-2 Postulated Flaw - Circumferential 4-3 Semielliptical.Surface Flaw 4-3 Shape Factors for Surface Flaws 4-4 4-4 Membrane Correction Factors for Surface Flaws 4-6 4-5 Bending Correction Factor for Surface Flaws 4-7 5-1 Fatigue Crack Growth Reference Law for Reactor 5-2 Vessel Steels ix
LIST OF TABLES TABLE TITLE PAGE 2-1 Material Properties 2-4 3-1 Secondary Side Design Transients 3-2 3-2 Schedule of Secondary Side Operating Transients 3-3 4-1 Inside and Outside Longitudinal Stresses 4-8 6-1 Stress Intensity Factor Ranges (AK 1 )
6-2 7-1 Results of Fatigue Crack Growth Evaluation 7-2 xi
SECTION 1 INTRODUCTION The linear elastic fracture mechanics approach to the design against failure is basically a stress intensity factor consideration in which criteria are established for fracture instability in the presence of a crack-like flaw. Consequently, a basic assumption in employing the fracture mechanics technology is that a crack or crack-like defect (either due to postulation or defective manufacture) exists in the structure being evaluated. By using the stress intensity factor, K1, all pertinent variables (flaw size, structural geometry and nominal stress) can be condensed into one parameter.
A necessary ingredient in the concept of fracture mechanics is know ledge of the present crack size. A fatigue crack growth evaluation will determine the growth of a flaw (either postulated or discovered during an in-service inspection) through end of life from the initial state.
This growth is a result of variations in the crack tip stress field due to coolant pressure and temperature changes during transients. The pro cedure for such a fatigue analysis involves finding the crack growth during each transient and adding this growth to the initial crack size.
This report presents the fatigue crack growth evaluation of the main steam line for San Onofre Unit 1, and the analysis results will be used in the mechanistic pipe break study of the main steam line with a postulated cir cumferential flaw. Since a circumferential flaw represents the most severe flaw orientation for the pipe break analysis, only circumferential flaws are considered in this fatigue crack growth evaluation.
The fatigue crack growth analyses presented herein were conducted in the same manner as suggested b Section XI, Appendix A of the ASME Boiler and Pressure Vessel Code[ 1.
The analysis procedure involves assuming an initial flaw exists at some point and predicting the growth of that flaw due to an imposed series of stress transients. The growth of a crack per loading cycle is dependent on the range of applied stress intensity factor AKI, by the following relation:
da Co(AK )n where "C" and the exponent "n" are. functions of material properties.
1-1
The input required for a fatigue crack growth analysis is basically the information necessary to calculate the parameter AKI, which de pends on crack and structure geometry and the range of applied.
stresses in the area where the crack exists. Once AKI is calculated, the growth due to that particular cycle can be calculated by equation (1-1).
This increment of growth is then added to the original crack size, and the analysis proceeds to the next transient. The procedure is continued in this manner until all the transients known to occur in the period of evaluation have been analyzed.
Crack tip stress intensity factors are calculated using semi-elliptic surface flaw expressions. Mechanical stresses and the thermal stress distribution through the thickness of the pipe are used in the calcu lation of the stress intensity factor K.
The technique.presented in this report is to determine the final crack depth for an assumed initial flaw postulated in the pipe wall.
The postulated initial crack depths range from 0.125 in. to 0.375 in. and are considered to realistically encompass the range of flaws that could be present.
1-2
SECTION 2 THERMAL AND STRESS ANALYSIS This section presents the results of the transient thermal and stress analysis of the main steam line for San Onofre Unit 1. The purpose of this analysis is to determine the stresses in the pipe due to the transient thermal and mechani cal loads identified in the applicable pressure vessel equipment specification.
2-1 ASSUMPTIONS The geometry of the main steam line is shown in figure 2-1.
The interior sur face of the pipe is in contact with the steam, and the resulting heat transfer coefficient is estimated as 400 8tu/hr-ft 2_.F based on the Dttus-Boelter[2]
forced convection correlation for all of the reactor design transients.
The outside surface is assumed to be insulated.
2-2 THERMAL ANALYSIS - TEMPERATURES AND STRESSES The heat transfer analysis for each of the transients was carried out by an explicit finite difference heat transfer analysis[3]. The temperature profiles generated by this analysis were then used to calculate thermal stresses. The equations for thermal stress in a hollow cylinder from Timoshenko and Goodier[4]
were used:
aE 1 2 a2 b
r radial stress =
ar r2 f Trdr - f Trdr)
(2-1) r b - a a
a (a2 2
b r.r tangential stress = a vr 1 r2 + a2 1 b
+
dr - Tr2' (2-2) r b - a a
a
=
( cE 2
b axial stress
=
2 -a 2 f Trdr - T)
(2-3) b -a a
where r = radial position T = temperature as function of r; T-+T(r) a = inner radius of the pipe b = outer radius of the pipe v = Poisson ratio aE = the product of the coefficient of thermal expansion and the modulus of Elasticity 2-1
0.968' 11.032"R Figure 2-1 San Onofre Unit 1 Main Steam Line 2-2
The integrals in equations (2-1) through (2-3) are evaluated numerically to provide the necessary thermal stresses for each of the transients analyzed.
2-3 MECHANICAL STRESS ANALYSIS The mechanical loading for the pipe results only from internal pressure, and since this is not a discontinuity region, the resulting stresses in the steam line were calculated in closed form:
(b + a ch.
2 2
(2-4) i (b - a 2) 2a2 ah = P (2-5) 0 (b2 -a 2 2
=
=
a (2-6) a i a
2 b
2 1 o (b2 - a2 )
where P = internal pressure a = inner wall radius b = outer wall radius ah = hoop stress a
a = axial stress i = inside surface o = outside surface The thermal and mechanical stresses are combined, and then linearized through the steam line wall thickness to allow for calculation of the applied stress intensity factor at any given time in a transient, as will be described in detail in Section 4.
In San Onofre Unit 1 plant, the material used in the main steam line is SA106 Grade B. Table 2-1 lists the mechanical and physical properties from ASME Section III*5] used in the analysis.
2-3
TABLE 2-1 MATERIAL PROPERTIES Property (500'F)
Material SA106 Grade B Young's Modulus (psi) 26.4 x 10 3
Density (lb/in. )
0.281 Conductivity (Btu/hr-in.-oF) 2.217 Heat Capacity (Btu/lb-oF) 0.132 Coefficient of Thermal Expansion 8.18 x 10-6 (in/in.-oF)
Poisson's Ratio 0.30 2-4
SECTION 3 DESIGN TRANSIENTS The design transients used in the fatigue evaluation of the main steam line pipe are given in table 3-1.
The transient conditions selected for this evaluation are based on conservative estimates of the magnitude and frequency of the temperature and pressure transients resulting from various operating conditions in the plant. These are representative of transient conditions which are considered to occur during plant operation and are sufficiently severe or frequent to be of significance to component cyclic behavior. Further, these are regarded as a conservative representation of transients which, when used as a basis for component fatigue evaluation, provide confidence that the component is appropriate for its application over the design life of the plant.
The total number of cycles for each operating transient exclusive of the pre operational test cycles has been assumed to be evenly divided over the 40-year operating life of the plant. The assumed schedular distribution of the reactor operating transients is shown in table 3-2.
3-1
TABLE 3-1 SECONDARY SIDE DESIGN TRANSIENTS TRANSIENT NUMBER OF OCCURRENCES Hot Standby 18300 Plant Loading and Unloading 18300 at 5% of Full Power/Minute Small Step Load Increase & Decrease 2000 Large Step Load Decrease 200 Loss of Power 40 Partial Loss of Flow 80 Loss of Load 80 Reactor Trip 400 TEST CONDITIONS Secondary Side Cold Hydro 5
3-2
TABLE 3-2 SCHEDULE OF SECONDARY SIDE OPERATING TRANSIENTS[a]
TRANSIENT NUMBER OF OCCURRENCES 5 Events 2 Events 1 Event 1 Every Per Year Per Year Per Year 4th Year Hot Standby 91 1
2 Plant Loading and 91 1
2 Unloading at 5% of Full Power/Minute Small Step Load Increase 10
& Decrease Large Step Load Decrease 1
Loss of Power 1
Partial Loss of Flow Loss of Load Reactor Trip 2
[a] This table does not include preoperational test cycles since they occur prior to plant operation.
SECTION 4 STRESS INTENSITY FACTOR CALCULATIONS This section describes the method of calculating the stress intensity factor KI using membrane and bending stresses. The stresses are determined by stress analysis as described in Section 3. Stresses resulting from pressure and thermal transients are considered in calculating the stress intensity factors. The actual stress distribution through the pipe wall is conservatively approximated by using the linearization technique illustrated in figure 4-1.
In this analysis, a circumferential flaw on the inside surface of the pipe is postulated. Crack depths varying from 0.125 inch to 0.375 inch have been in cluded to determine the sensitivity of the results to the initial assumed flaw depth. The initial flaw depth of 0.375 inch represents a 39% through wall flaw.
A semielliptical configuration with length-to-depth ratio of six and its major axis on the surface is assumed for the shape of the flaw as shown by figure 4-2.
4-1 K1 EXPRESSION The stress intensity factor KI at the point of maximum depth is calculated from the membrane and bending stresses using the following equation from Section XI of the ASME Code[1].
K1 = /'
(am Mm + ab Mb)
(4-1) where am2 b = membrane and bending stress, respectively a
= minor semiaxis (flaw depth)
Q
= flaw shape parameter including a plastic zone correction factor for plane strain conditions, (see figure 4-3).
2 2
S-0.212 (Ways)
= r/2 2
2 1-2 ) sin p do 0
b cys
= yield strength of material a
=
m + ab 4-1
INSIDE OUTSIDE SURFACE SURFACE EQUIVALENT LINEAR REPRESENTATION OF STRESS DISTRIBUTION ACTUAL NONLINEAR STRESS DISTRIBUTION Figure 4-1.
Linearized Representation of Stresses 4-2
Figure 4-2.
Postulated Flaw -
Circumferential Semielliptical Surface Flaw 4-3
0.5
_0.4 1.0 o
0.8 00..
- r.
0.3 1 0.2 0.0
-LJ 0..I U
0.0 0.0 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0.
2.2 2.4 FLAW SHAPE PARAMETER (Q)
SURFACE FLAW Figure 4-3 Shape Factors for Surface Flaws 4-4
b
= major semiaxis (flaw length/2)
= parametric angle of the ellipse Mm
= correction factor for membrane stresses (see figure 4-4)
Mb
= correction factor for bending stresses (see figure 4-5)
The inside and outside stresses for each transient for the three regions analyzed are given in table 4-1.
The stress values which yield both the maximum and the minimum KI values for each transient are listed.
4-5
2.0 T= 0.0 F=0.05 j
0.1
'.9
-a a
1.7 -=
0.2 1.6 C:
.5 S1.5 0.3 1.2 0.35 <
<0.5 1.1 1.0 I
I I
I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 FLAW DEPTH-TO-THICKNESS (-) RATIO t
Figure.4-4 Membrane Correction Factors for Surface Flaws 4-6
1.6 a/
0.0 1.2 1.0
_al
= 0. 3
- 00.
- 0. -
a/
=0.
0.6 00o2 NNIN.
LEGEND:0.
.L0.3 0.4 EXACT SOLUTION (
00)D
--- ESTIMAT.E (p = 00) 0.4 ESTIMATE (p = 900)0.
0.2 0.0 000
- 0. I 0.2 0.3 0.4
- 0.
5 0.6 FLAW DEPTH TO THICKNESS RATIO (alt)
Figure 4-5 Bending Correction Factor for Surface Flaws 4-7
TABLE 4-1 INSIDE AND OUTSIDE LONGITUDINAL STRESSES q Inside[a]
a Outside[a]
a Inside[b]
a Outside[b]
Transient (ksi)
(ksi)
(ksi)
(ksi)
Hot Standby 5.164 5.100 3.933 3.939 Unit Loading and.
5.096 5.013 3.421 3.715 Unloading Small Step Load Increase & Decrease 4.024 3.866 3.638 3.785 Large Step Load Decrease 4.340 4.248 3.452 4.541 Loss of Power 5.184 4.612 3.817 3.817 Partial Loss of Flow 4.511 4.511 3.341 4.798 Loss of Load 4.996 4.996 2.773 6.054 Reactor Trip 4.038 3.106 1.705 1.705 Cold Hydro 8.092 8.092 0.000 0.000
[a] These stress values lead to maximum K1I
[b] These stress values lead to minimum KI
SECTION 5 FATIGUE CRACK GROWTH RATE The growth of a crack per loading cycle is dependent on the range of applied stress intensity factor AKI, by the following relations:
-= C (AK )n (5-1) where "C 0 and the exponent "n" are functions of material properties.
5-1 ASME SECTION XI CRACK GROWTH LAW FOR WATER REACTOR ENVIRONMENT The upper bound curve from ASME Section XIElJ for fatigue crack growth analysis shown by figure 5-1 is considered applicable to SA106 Grade B material in this analysis based on the following justification provided in Reference [6].
The reference law in the ASME Code Section XI was designed to be applicable to car bon and low alloy steels to minimum yield strengths less than or equal to 50 ksi, although no data were available at the time of its inception to support such a wide application [6].
Data are now available to demonstrate that medium strength carbon and low alloy steels do indeed have very similar behavior in a water en vironment. Besides the original test materials of A508 Cl 2 and A533B Cl 1 there are test results available for ASTM A516 GR-70 steel in light water reactor en vironment which agree well with the reactor vessel steels[7.
This steel has a minimum specified yield strength of 38 ksi.
Further data in water environments have been obtained by Soctt [8] on lower strength steels and Vosikovsky [9] on higher strength line pipe steel (65 ksi minimum yield strength).
This informa tion suggests that the reference curve should have applicability to all carbon and low alloy steels with minimum yield strength less than 65 ksi.
The reference law in the ASME Code Section XI is represented by the following expression.
dal
= (0.3795 x 10-3) AK 3.726 (5-2) da
- where,
= Crack growth rate, micro-inches/cycle AK = stress intensity factor range, ksi/in = (KI max - KI min)
KI max' KI min Maximum and Minimum KI respectively computed during the transient 5-1
io3 8
6 4
2 SURFACE FLAWS (WATER REACTOR ENVIRONMENT)
~1 da 2
(0.3795 X 10-3) AK 3.726 (j
dN LU 8
5
- 6.
0 A;
2 D
10 6
I4*
NOTE:
FROM ASME CODE.
SECTION fL 2
100 100 2
4 6 8 10' 2
4 6
8 102 STRESS INTENSITY FACTOR RANGE. !IKI (KSI
'N)
Figure 5-1.
Fatigue Crack Growth Reference Law for Reactor Vessel Steels 5-2
SECTION 6 FATIGUE EVALUATION The fatigue crack growth analysis presented herein has been conducted in the same manner as suggested by Section XI Appendix A of the ASME Boiler and Pressure Vessel Code[l].
The analysis procedure involves postulating an initial circumferen tial flaw and predicting the growth of that flaw due to an imposed series of stress transients. The input required for a fatigue crack growth analysis is basically the information necessary to calculate the parameter AKI which depends on crack and structural geometry and the range of applied stresses in the area where the crack exists. Once AKI is calculated, the growth due to that particular cycle can be calculated by equation 4-1.
This increment of growth is then added to the original crack size, and the analysis proceeds to the next transient. The procedure is continued in this manner until all the transients known to occur in the period of evaluation have been analyzed.
In order to determine the maximum potential for fatigue crack growth of the postu lated flaw in the pipe during normal operation, a cumulative fatigue crack growth analysis is performed. All design transients are considered in chronological order according to the assumed schedule prescribed in table 3-2. Stress intensity factors are determined for each transient using the bounding semielliptical flaw model and the method for KI determination outlined in Section 4. Each transient is evaluated in the following manner:
- 1) Determine the maximum range of KI fluctuation (AKI associated with the transient).
- 2) Find the incremental flaw growth (Aa) corresponding to AKI from the fatigue crack growth rate data.
- 3) Update the flaw size by assuming the flaw grows to a geometrically similar, larger flaw with a minor half axis (a + Aa).
- 4) Proceed to the next transient.
The above procedure, after all transients have been considered, yields the expected end-of-life flaw size (af). The procedure has been automated and the crack growth results are obtained for 0.125 inch, 0.250 inch, and 0.375 inch postulated initial flaw depths. The stress intensity factor ranges (AK
- 1) associated with the transients are presented in table 6-1.
6-1
TABLE 6-1 STRESS INTENSITY FACTOR RANGES (AK 1 )
No.
Transient Postulated AKI Flaw Depth (in.)
(ksi/in) 1 Hot Standby
.125
.765
.250 1.143
.375 1.546 2
Unit Loading and Unloading
.125 1.024
.250 1.509
.375 2.016 3
Small Step Load Increase
.125 0.223 and Decrease
.250 0.312
.375 0.397 4
Large Step Load Decrease
.125
.485
.250
.639
.375
.765 5
Loss of Power
.125
.820
.250 1.189
.375 1.564 Partial Loss of Flow
.125
.644
.250
.859
.375 1.039 7
Loss of Load
.125 1.194
.250 1.548
.375 1.816 6-2
TABLE 6-1 (cont'd)
STRESS INTENSITY FACTOR RANGES (AK1 )
Postulated AK No.
Transient Flaw Depth (in.)
(ksillin) 8 Reactor Trip
.125 1.402
.250 2.035
.375 2.681 9
Cold Hydro
.125 5.068
.250 7.606
.375 10.326 6-3
SECTION 7 RESULTS AND CONCLUSIONS A fatigue crack growth analysis has been carried out for the main steam line pipe of San Onofre Unit 1, and the results of the analysis are summarized in table 7-1.
This table presents the fatigue crack growth results for a range of postulated flaw depths oriented circumferentially. The postulated flaws are assumed to be six times as long as they are deep. Based on these re sults, it is concluded that growth by fatigue is negligible.
7-1
TABLE 7-1 RESULTS OF FATIGUE CRACK GROWTH EVALUATION Postulated Crack Depth (in) After Year Initial Crack Depth (in) 10 20 30 40 0.125 0.12500 0.12501 0.12501 0.12501 0.250 0.25002 0.25003 0.25004 0.25005 0.375 0.37505 0.37508 0.37511 0.37515 7-2
SECTION 8 REFERENCES
- 1. ASME Boiler and Pressure Vessel Code,Section XI, Appendix A, "Analysis of Flaw Indications", American Society of Mechanical Engineers, New York, 1980 Edition.
- 2. Dttus, F. W. and Boelter, L. M.K., "Heat Transfer in Automobile Radiators of the Tubular Type", California University Publication in Eng. 2, No. 13, 443-461, 1930.
- 3. Holman, J. P., Heat Transfer, McGraw Hill Book Company, New York, 1963.
- 4. Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, 3rd Edition, McGraw Hill Book Company, New York, 1970.
- 5. Appendix I to the ASME Boiler and Pressure Vessel Code, Section-III, Division 1, Subsection NA, "Design Stress Intensity Values, Allowable Stresses, Material Properties, and Design Fatigue Curves", American Socitty of Mechanical Engineers, New York, 1980 Edition.
- 6. Bamford, W. H., "Application of Corrosion Fatigue Crack Growth Rate Data to Integrity Analysis of Nuclear Reactor Vessels", Transactions of the ASME, Vol.
101, pp. 184-190, July 1979.
- 7. Hale, D. A., Yuen, J. and Gerber, T., "Fatigue Crack Growth in Piping and Reactor Pressure Vessel Steels in simulated BWR Environment", GEAP-24098/NRC-5, General Electric Co., Jan. 1978.
- 8. Scott, P. M. and Silvester, D. R. V., "The Influence of Mean Tensile Stress on Corrosion Fatigue Crack Growth in Structural Steel Immersed in Seawater",
Tech. Report UKOSRP 3/02, Harwell Corrosion Service, UKAEA, May 1977.
- 9. Vosikovsky, 0., "Fatigue Crack Growth in an X-65 Line Pipe Steel at Low Cyclic Frequencies in Aqueous Environments", ASME Journal of Engineering Materials and Technology, Oct. 1975, pp. 298-304.
8-1