ML20213D726
| ML20213D726 | |
| Person / Time | |
|---|---|
| Site: | South Texas  |
| Issue date: | 10/31/1986 |
| From: | Bamford W, Roarty D, Swamy S WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML19292G221 | List: |
| References | |
| WCAP-11328, NUDOCS 8611120208 | |
| Download: ML20213D726 (56) | |
Text
MESVENGHOUSE CLASS 3 WCAP-11328 l
l CUMULATIVE USAGE FACTOR CRITERION FOR BREAK POSTULATION FOR SOUTH TEXAS UNITS 1 AND 2 October 1986 I sid W. H. Bamford D. H. Roarty 1 -
S. A. Swamy F. J. Witt t, Verified by: E. R. Johnson Approved by: , [M
- 5. 5/Palusamy, Manager Structural Materials Engineering
~
WESTINGHOUSE ELECTRIC CORPORATION NUCLEAR ENERGY SYSTEMS P.O. Box 2728 Pittsburgh, Pennsylvania 15230 b
A A
l TABLE OF CONTENTS Section Title Page 1 INTRODUCTION 1-1 2 TRANSIENTS AND THERMAL STRESS ANALYSIS OF A TYPICAL ACCUMULATOR LINE 2-1 2.1 Critical Location for Fatigue Crack Growth Analysis 2-1 2.2 Design Transients 2-2 2.3 Simplified Stress Analysis 2-3 2.4 Stress Distribution for Severe Transients 2-5 2.5 OBE Loads 2-6 2.6 Total Stress for Fatigue Crack Growth 2-6 3 FATIGUE CRACK GROWTH ANALYSIS OF THE TYPICAL ACCUMULATOR LINE 3-1 3.1 Analysis Procedure 3-1 3.2 Crack Growth Results 3-4 4 CALCULATION OF CUMULATIVE USAGE FACTOR 4-1 5 APPLICABILITY TO OTHER LINES 5-1 5.1 Effect of Loadings On Fatigue Crack Growth 5-1 5.2 Evaluation of Transient Loadings 5-2 6 HISTORY OF CORROSION CRACKING 6-1 7 CONSIDERATION OF PUMP VIBRATIONS 7-1 7.1 Estimate of Fatigue Threshold Stress Intensity Range 7-1 7.2 Calculation of Stress Intensity Factors for Vibrating Loads 7-3 iii
\
TABLE OF CONTENTS (cont.)
Section Title Pa2' 7.3 Stress Limits from Vibratory Monitoring 7-3 7.4 Interaction of Flaw Size, Alternating Stress and Stress Intensity Factor in the Vibratory :
Range 7-4 7.5 Comparison of the Alternating Stress of 7.5 psi with Plant Measurements 7-5 8 USE OF C INDICES IN FATIGUE CRACK GRDWTH ANALYSIS 8-1 9 DISCUSSION AND CONCLUSIONS 9-1 10 REFERENCES 10-1 j
.{
iv
LIST OF TABLES I
Table Title Page 2-1 Thermal Transients Considered for. Fatigue Crack Growth Evaluation 2-7 2-2 Stresses for the Minor Transients (psi) 2-8 -
2-3 Accumulator Line Envelope Loads 2-9 5-1 Summary of Auxiliary Line Pipe Break Locations 5-4 5-2 Evaluation of Significant Transients 5-5 -
L 7-1 Values of AK 7-7 th fr m Usami (Reference 7-5) l v
LIST OF FIGURES Figure Title Page 1-1 Schematic Diagram of a Typical Accumulator Line Showing Critical Locations 1-4 2-1 Comparison of Typical Maximum and Minimum Stress Profile [
Ja,c.e 2-10 2-2 Schematic of Accumulator Line at [
Ja,c.e 2-11 3-1 Reference Crack Growth Rate Law (with Data) Used for Calculations 3-5 3-2 Crack Propagation after Initiation - Typical Accumulator Line Cumulative Usage Factor = [ Ja,c.e 3-6 7-1 Threshold Fatigue Crack Growth Data for 304 Stainless Steel 7-8 7-2 Relationship Between Alternating Stress and Postulated Flaw Depth at which the Threshold Stress Intensity Range is ( )*'C 7-9 7-3 Relationship Between the Range of Stress Intensity Factor and the Alternating Stress for Postulated Flaws in an Example Piping System 7-10 8-1 Stress Distribution at a Tapered Transition Joint l Due to an Axial Load 8-4 vii
SECTION 1 INTRODUCTION ,
In the design of the Class 1 piping components in a Pressurized Water Reactor (PWR), a cumulative usage factor (CUF) for each Class 1 piping component is calculated using Section III of the ASME Code. To ensure adequate design margin for the plant lifetime (40 years) for fatigue, each of these CUF values is required to be less than 1.0. Also during the design, construction, and testing of a PWR, significant effort is devoted to reviewing the effects of postulsted ruptures of high energy piping. The NRC Standard Review Plan (SRP)
(Reference 1-1) provides a methodology for defining those joints in Class 1 piping systems where breaks are postulated to occur. This methodology specifies that breaks be postulated where either the ASME Code Section III E fatigue CUF exceeds 0.1 or the ASME Code equations 10,12, or 13 stress intensity range is greater than 2.4 S ,.
The South Texas Project piping analysis completed by Bechtel Energy Corporation has identified [ ]a,c.e locations where the CUF exceeds 0.1. Using the SRP guidance, the designer would postulate a circum-ferential and/or longitudinal break at each location. Evaluation of damage due to pipe whipping and discharging fluids must then be perfcrmed. If components needed to bring the plant to a safe shutdown condition are adversely impacted, then these items must be protected. The standard means of protection are the design and installation of pipe whip restraints and/or fluid jet impingement barriers. Due to the large loads resulting from postu-lated pipe breaks, these pipe whip restraints and jet impingement barriers are massive additions to the nuclear plant. This protective hardware occupies large amounts of space and results in plant congestion. The reduction in space for maintenance and inspection results in increased man rem irradiation exposures and decreased effectiveness of in-service inspections of the piping components. This is of particular concern since the area where the CUF is larger than 0.1 is in Class 1 piping inside the containment building.
1-1
The American Nuclear Society Working Group on Pipe Break (ANS-58.2) has proposed increasing the CUF criteria for pipe break postulation from 0.1 to a value of 0.4. This increased value, if used, would result in a significant reduction in the number of postulated Class 1 pipe breaks. Specifically for -
South Texas there are [ la,c.e locations in Class 1 piping where the CUF is between 0.1 ahd 0.4. Deleting these [ )**C postulated breaks from the design is expected to eliminate approximately [ ]a.c.e associated pipe whip restraints and jet impingement barriers.
This report has been prepared in support of revising the cumulative usage factor screening criterion for break postulation in the South Texas Project Units 1 and 2 piping systems from 0.1 to 0.4 This subject was discussed with the NRC staff in several meetings. In the meeting of October 15, 1986, the staff requested documentation of specific arguments in support of the CUF screening criterion revision. The documentation is provided in this report.
Included in this report is a consideration of the tolerance of a typical accumulator line piping system for the presence of small cracks, which demonstrates that such a flaw would take many plant lifetimes to penetrate the wall (Sections 2 and 3). The accumulator injection line chosen for illustration of the margins which exist in a typical PWR plant is shown in Figure 1-1. The most limiting region for fatigue crack growth in this accumulator line was found to be at the [
Ja,c.e Both these systems are of stainless steel, and the evaluation will be concentrated on this location as shown in Figure 1-1. A brief summary of the methodology used to calculate the usage factor of [ la.c.e at the accumulator line weld joint is provided in Section 4. This calculation utilized standard ASME Section III techniques consistent with those utilized on the South Texas Project Class 1 piping. A discussion of the bases for applying the sample accumulator line fatigue crack growth calculations to the South Texas Project Class 1 piping is included in Section 5. The sample calculation was performed on a typical PWR accumulator line with operational transients and pipe size similar to those of the South Texas Project plants. It is demonstrated that the significant loadings in the 1-2
accumulator line calculations are applicable to the South Texas Project Class 1 piping. Thus, the results of the typical accumulator line calculations are shown to envelope the South Texas Project Class 1 lines for which relief is requested. I ~
A discussion on the history of cracking and an evaluation of the susceptibil-ity of the PWR Class 1 auxiliary lines to stress corrosion cracking is presented (Section 6). In Section 7 the impact of vibratory stresses is examined and a comparison is made between vibratory stresses obtained from measurements made on actual plants and threshold values. The use of C stress indices in the fatigue crack growth (FCG) analysis is discussed in Section 8.
The C stress indices modify the calculated stresses such as P/A and M/Z to reflect stress distribution which differ from a straight pipe section remote from discontinuities.
The results of the fatigue crack growth analysis for a typical accumulator line given in Section 3 show significantly larger lifetimes than would have been estimated based on previously published analysis by other investigators such as that in NUREG-3059 (Reference 1-2). This variation is accounted for by the use in the older work of a very conservative threshold ak value and upper bound crack growth rate curves in the Reference 1-2 analysis. Also, the Reference 1-2 work used an arbitrary end of-life flaw depth of t/4 in the analysis. As can be shown by reviewing Figure 3-2 of this report, stopping at t/4 significantly reduces the lifetimes to go through wall. The FCG methodology used in this report is considered to provide a more realistic crack growth estimate for the South Texas Project Class 1 piping.
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SECTION 2 TRANSIENTS AND THERMAL STRESS ANALYSIS OF A TYPICAL ACCUMULATOR LINE The thermal transient stress analysis was performed to obtain the through wall stress profiles for use in the fatigue crack growth analysis of Section 3.
The through wall stress distribution for each transient was calculated for i) the time corresponding to the maximum inside surface stress and, ii) the time corresponding to the minimum inside surface stress. These two stress profiles are called the maximum and minimum through wall stress distribution, respectively. The constant stresses due to pressure, deadweight and thermal expansion (at normal operating temperature, 550*F) loadings were superimposed on the through wall cyclical stresses to obtain the total maximum and minimum stress profile for each transient. Linear through wall stress distributions were calculated by conservative simplified methods for all minor transients.
More accurate nonlinear through wall stress distributions were developed for the more severe transients by finite element analysis.
2.1 Critical Location for Fatigue Crack Growth Analysis The accumulator line stress reports, design thermal transients (Section 2.2),
one-dimensional (1-D) analysis data on accumulator line thermal transient stresses (based on ASME Section III NB3650 rules) and the geometry were reviewed to select the worst location for the fatigue crack growth analysis.
The [
Ja,c.e was determined to be the most critical location for the fatigue crack growth evaluation. This location is selected as the worst location based on the following considerations:
i) the stress due to thermal expansion is high; ii) the effect of discontinuity due to undercut at the weld will tend to inc'rease the cyclical thermal transient loads; 2-1
iii) the review of data shows that the 1-D thermal transient stress 6s in the accumulator line piping section are generally higher near the [
ja c.e 2.2 Design Transients The transient conditions selected for this evaluation are based on conserva-tive estimates of the magnitude and the frequency of the temperature fluctua-tions resulting from various operating conditions in the plant. These are representative of the conditions which are considered to occur during plant operation. The fatigue evaluation based on these transients provides confidence that the component is appropriate for its application over the design life of the plant. All the normal operating and upset thermal transients, in accordance with the design specification and the applicable system design criteria document, were considered for this evaluation. Out of these, only 15 transients were used in the final fctigue crack growth analysis as listed in Table 2-1. These transients were selected on the basis of the following criteria:
( (2-1) ja.c.e (2-2) where,
(
ja.c.e 2.3 Simplified Stress Analysis The simplified analysis method was used to develop conservative maximum and minimum linear through-wall stress distributions due to thermal transients, in this method, a 1-D, heat transfer computer program was used to perform the 2-2 l
transient thermal analysis to determine the through-wall temperature gradients as a function of time. The inside surface stress was calculated by the following equation [
ja.c.e The maximum and minimum inside surface stresses were obtained from the S g values calculated for each time step of the transient solution.
2-3
The outside surface stresses corresponding to maximum and minimum inside stresses were calculated by the following equations:
[ (2-7)
Ja.c.e (2-8) where,
[
a ,c.e 7
All other parameters are as defined previously.
The material properties for the accumulator pipe [ la,c.e and the [ la.c.e were taken from the ASME Section III 1983 appendices ~at the normal operating temperature (550*F) of the accumulator line. The values of E and a, at the normal operating temperature, provide a conservative estimation of the through wall thermal transient stresses as compared to room temperature properties. The following values were conservatively used, which represent the highest of the [
la,c.e materials:
[
,f..c.e 2-4
The maximum and minimum linear through wall stress distribution for each thermal transient was obtained by joining the corresponding inside and outside surface stresses by a straight line. The simplified analysis discussed in this section was performed for all minor thermal transients of Table 2-1 (1 through 9, 13, and 15). Nonlinear through wall stress profiles were developed for the remaining more severe transients as explained in Section 2.4. The inside and outside surface stresses calculated by simplified methods for the minor transients are shown in Table 2-2. The comparison of the through-wall stress profile, computed for a typical transient by the simplified method and that based on the detailed finite element analysis, is shown in Figure 2-1. This figure shows that the simplified method is more conservative for fatigue crack growth applications.
2.4 Stress Distribution for Severe Transients The nonlinear stress distributions were developed for the severe transients, i.e., transients 10, 11, 12, and 14. As mentioned earlier, the accumulator line section near the [ Ja.c.e is the worst location for fatigue crack growth analysis. A schematic of the accumulator line geometry at this location is shown in Figure 2-2. The [
]a c.e The cross-sectional dimensions corresponding to reduced thickness, as shown for the critical section in Figure 2-2, were used in this model. This simplified model computes nonlinear through-wall stress distribu-tion but does not include the effect of the discontinuity. The effect of the discontinuity at the critical section (Figure 2-2) was included by increasing the magnitude of the nonlinear through wall stress by (
Ja,c.e of the pipe wall. This amplification is based on a previous transient analysis of a RCS nozzle utilizing both a detailed model of the complete nozzle and attached pipe and a simplified model as described above. Identical transients were run using both models.
Comparison of the results shows that for the inside four nodes the average 2-5
ratio of detailed model stress to simplified model stress is (
Ja.c.e was therefore conservatively chosen.
2.5 OBE Loads The stresses due to DBE loads were neglected in the fatigue crack growth analysis since these loads will not contribute significantly to crack growth due to small number of cycles.
2.6 Total Stress for Fatigue Crack Growth The total through-wall stress at a section was obtained by superimposing the pressure load stresses and the stresses due to deadweight and thermal expansion (normal operating case) on the thermal transient stresses (of Table 2-2 or the nonlinear stress distributions discussed in Section 2.4). Thus, the total stress for fatigue crack growth at any point is given by the following equation:
a,c.e (2-9)
The envelope thermal expansion, deadweight and pressure loads for calculatir.g the total stresses of Equation (2-9) are summarized in Table 2-3.
2-6
TABLE 2-1 THERMAL TRANSIENTS CONSIDERED FOR FATIGUE CRACK GROWTH EVALUATION Trans. No. of No. Description Occurrences 1 a,c.e 2
3 4
5 6
7 8
9 10 11 12 13 14 15 i
8, 2-7
0, -
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TABLE 2-3 ACCUMULATOR LINE ENVELOPE LOADS Condition Loads at Location A (for each of the loops) ,
F a gb p g p g 7 y (kips) (in-kips) (kips) (in-kips) (kips) (in-kips) (kips) (in-kips)
Normal Load { ]a,c.e (High Pressure Region) l 7
e a
F is axial force; internal pressure load is not included b
M is bending moment c
Used in the FCG analysis
a.c.e a.
Figure 2-1: Comparison of Typical Maximum and Minimum ggegs Profile Computed bySimplifiedand[ ]
2-10
- - a ,c.e 1.
- 2. L _
_ - . a ,c.e Accumulator Pipe Figure 2-2: Schematic of Accumulator Line at [ ]a,c.e 2-11
\ ______-
SECTION 3 FATIGUE' CRACK GROWTH ANALYSIS OF THE TYPICAL ACCUMULATOR LINE The fatigue crack growth analysis was performed to determine the effect of the design thermal transients in Table 2-1. The analysis was performed for the critical cross section of the model which is identified in Figure 2-2. A crack depth corresponding to that which might develop under fatigue cycling was postulated and was subjected to the transients in Table 2-1. [
ja,c.e !
3.1 Analysis Procedure 1
The fatigue crack growth analyses presented herein were conducted in the same manner as suggested by Section XI, Appendix A of the ASME Boiler and Pressure Vessel Code. 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 AKy by the following relation:
i h=CoaK;" (3-1) ,
where "Co" and the exponent "n" are material properties, and AK is g !
defined later in Equation (3-3). For inert environments these material properties are constants, but for some water environments they are dependent on the level of mean stress present during the cycle. This can be accounted for by adjusting the value of "Co" and "n" by a function of the ratio of minimum to maximum stress for any given transient, as will be discussed later. Fatigue crack growth properties of stainless steel in a pressurized water environment were used in the analysis.
3-1
The input required for c fatigue crack growth analysis is basically the information necessary to calculate the parameter AK ,g which depends on crack and structure geometry and the range of applied stresses in the area wherethecrickexists. Once AKgis calculated, the growth due to that ;
particular cycle can be calculated by Equation (3-1). This increment of growth is then added to the original crack size, the AKg adjusted crack size, and the analysis proceeds to the next transient. The procedure is continued in this manner until all the transients have been analyzed.
The crack tip stress intensity factors (K )g to be used in the crack growth analysis were calculated using an expression which applies for a semi-elliptic surface flaw in a cylindrical geometry (Reference 3-1). The stress intensity factor expression was calculated using the actual stress profiles at the critical section. The maximum and minimum stress profiles corresponding to each transient were input, and each profile was fit by a third order polynomial:
o(x)=A+A({}+A()+A({}
0 y 2 3 (3-2)
The stress intensity factor K;(e) was calculated at the deepest point of the crack using the following expression:
2 2 (cos 4 + sin ,)0.25(A H00+ AyHy K(#)=((%)
g (3-3) 3 1 a2
+yp2 2*EP3 A H )3,,c,,
4 a A H 3 where [
3a,c.e 3-2
[
ja.c.e Calculation of the fatigue crack growth for each cycle was then carried out using the reference fatigue crack growth rate law determined from considera-tion of the available data for stainless steel in a pressurized water environment. This law allows for the effect of mean stress or R ratio (KImin/KImax) on the growth rates.
The reference crack growth law for stainless steel in a pressurized water j environment was taken from a collection of available data (Reference 3-2) l since no code curve is available, and it is defined by the following equation:
[
ja,c.e The reference crack growth law, along with all the supporting data, is provided in Figure 3-1. It can be seen that the supporting data included both forged and cast base metal, and associated welds, tested in a PWR environment.
~
3-3 l
f 3.2 Crack Growth Results The analysis was carried'out for the critical cross section described earlier, andassumeda5initialflawdepthof[ la,c.e The length was six times the depth, and this shape was assumed to remain constant throughout the crack growth calculation.
The results of the crack growth calculation are provided in Figure 3-2. This figure shows that the fatigue crack growth progresses very slowly in the accumulator line, even at the most limiting location. For the flaw to progress to a depth of [ ]a,c.e over seven lifetimes, or 280 years. As the crack progress deeper into the wall, the growth tends to slow down somewhat, because the inside surface stresses have less of an effect. The crack actually reaches [ ]a,c.e at approximately [ la,c.e lifetimes.
3-4
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- Knax(1-R)05(NPa6) 10 100 10-3 _
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' lo . . 100 K,gg.K,,,(g.g}o.s gs; g _
FIGURE 3-1 REFERENCE CRACK GROWTH RATE LAW (WITH DATA) USED FOR CALCULATIONS 3-5
a,c.e j'
l i
4 i
I Figure 3-2: Crack Propogation after Initia},g,- i Typical Accumulator Line CumulativeUsageFactor=[ ]
t 3-6
SECTION 4 CALCULATION OF CUMULATIVE USAGE FACTOR The cumulative usage factor (CUF) for ASME Section III Code (Reference 4-1) designs for Class 1 piping is calculated using the methods and requirement of the Code. The Code utilizes the maximum shear stress theory to determine a stress intensity (2 times maximum shear) for each stress cycle. An allowable number of cycles is then calculated using the fatigue curve provided in Appendix I of the Code. The damage (usage factor) is then calculated considering the postulated number of occurrences for the loadset. Finally,
" Miner's Rule" is used to determine the total (cumulative) fatigue usage by a linear sum of the incremental usage factors of each loadset. The weld joint on the accumulator piping was evaluated using these techniques. I Thermal transient stresses for the fatigue calculation were obtained using a two-dimensional finite element model including the nozzle and a portion of the attached pipe. Moment and pressure stresses were cbtained using standard Code NB-3650 techniques. The evaluation resulted in a cumulative usage factor of
[ ]a,c e In section 5 of this report there is a discussion of the loadings on the piping joint. This will provide a basis for the applicability of the fatigue crack growth at this point to the other Class 1 piping joints.
I l
I 4
4-1
i SECTION 5 APPLICABILITY TO OTHER LINES This section will describe the basis for applying the accumulator line fatigue i l
crack growth calculation to the Class 1 piping systems with cumulative usage factors between 0.1 and 0.4 on the Scuth Texas Project. The first step will be to establish which loadings control the fatigue crack growth in a typical example. Next, the critical loadings will be compared between the sample accumulator line and the Class 1 piping covered by this report.
5.1 Effect of Loadings on Fatigue Crack Growth The total stress in the fatigue crack growth (FCG) evaluation results from a
)
combination of pressure, moment, and thermal transients as illustrated by !
Equation 2-9. The moment and pressure stresses are normally restricted to reasonably low values by the ASME Code requirements and design practice. ;
Typically, in PWR Class 1 piping nominal axial pressure stresses are less than l
[ Ja,c.e and moment stresses are generally less than [
Ja,c.e .
In addition, the design basis for a PWR restricts the number of full range occurrences of these loadings to [ Ja,c.e cycles. This means that by themselves, moment and pressure stresses will have a negligible effect on FCG. However, thermal transient stresses are much less restricted in terms of magnitude. Stresses of [ Ja,c.e psi elastically calculated at the inside surface for a single event with more than 200 cycles are not unusual for locations with high cumulative usage factors. For the significant transients in the accumulator line analysis, in terms of FCG, the combined pressure and moment stress was less than [ ]a,c.e of the maximum stress.
The lower stresses of the pressure and moment loadings permit the assessment of the applicability of the accumulator line FCG calculation to other locations considering only the thermal transient loadings.
5-1
5.2 Evaluation of Transient Loadings It has been established'in Section 5.1 that the fatigue crack growth for typicalPWR61 ass 1pipingiscontrolladprimarilybythermaltransient loadings. This section will discuss why the transients used in the accumulator line analysis are representative of the transients for the South Texas Class 1 piping.
Table 5-1 summarizes the lines where revised usage factor pipe break criteria are being sought. Based on the previous arguments, the applicability of the accumulator line evaluation to South Texas can be established if the transients used in that evaluation cover the applicable South Texas transients for the auxiliary systems piping. Although the only quantitative way to do this is to evaluate the fatigue crack growth at each location, this is not required since a very large margin was demonstrated for the accumulator line weld (see Section 3). With this amount of margin it is not required to prove that the accumulator analysis enveloped all points on South Texas, rather it is sufficient to demonstrate that the accumulator transient loadings are representative of the applicable transient loadings on South Texas.
Since only an approximation of the transient loadings is required a very simple approach has been developed to compare the loadings. First, the significant transients are obtained from the applicable design document (Reference 5-1). A transient is assumed to be significant if the temperature change is greater than ( la,c.e and occurs'at a rate greater than
( Ja,c.e per second. Transients of smaller magnitude than this will not cause noticeable fatigue crack growth unless the number of cycles is very large. This occurs only on the pressurizer surge line which is addressed in separate detailed leak-before-break reports (References 5-2 and 5-3).
For each significant transient the fluid temperature change (DT) and number of cycles (N) is noted. The severity of transient loadings (S) is quantified by summing the product of DT and N for the transients:
5-2 I
i=n S= I DTgN$ (5-1) i=1 where n is the number of significant transients.
Table 5-2 provides the results of this evc.luation. Note that a factor of
[ ]a,c.e was applied to transients which contained a long ramp temperature change. This was done for the charging line transients to improve the accuracy of the comparison. Maximum stresses from analysis of a typical PWR charging line were reviewed to determine this factor. It was found that [ ]a,c.e was probably justified but [ Ja,c.e was conservatively chosen to use here.
Comparing the accumulator line to all the other South Texas Class 1 lines indicates that the loadings used in the FCG analysis are applicable to South Texas. The worst case appears to be the charging line with a factor of about
[ ]a,c.e increase. This number is probably a very high estimate since it is primarily due to a high number of cycles of a lower DT transient [
]a,c.e It is known that FCG follows a relationship which weighs stress changes to a power of approximately 4.5 rather than linearly (power of 1.0).
Taking this into consideration would reduce the magnitude of this transient
[ Ja,c.e to an almost insignificant relative affect.
In conclusion, the fatigue crack growth analysis on the typical accumulator line is clearly representative of fatigue crack growth which would be calculated for high usage factor points on South Texas Project lines. The margin demonstrated for the accumulator line is more than sufficient to cover the assumptions required in this evaluation.
5-3
TABLE 5-1
SUMMARY
OF AUXILIARY LINE PIPE BREAK LOCATIONS System ID No. of Breaks Line Size CUF Range Normal Charging to Loop 1 3 4 .12 to .17 Alternate Charging - Loop 3 4 4 .14 to .26 Aux. Press Spray 2 2 .12 to .19 Excess Letdown Loop 4 3 2 .12 to .26 Pressurizer Surge 14 16 .10 to .35 Spray Line 2 6 .34 to .39 SI Injection Loop 1 11 12 .11 to .21 SI Injection Loop 2 11 12 .11 to .16 SI Injection loop 3 7 12 .10 to .29 5-4 1
TABLE 5-2 EVALVATION OF SIGNIFICANT TRANSIENTS Auxiliary Line Transient Description DT(*F) 1 IDT
- N 1
- a C,e
.?
I w
I f
.0 I'
T 5-5
SECTION 6 HISTORY OF CORROSION CRACKING The Westinghouse reactor coolant system primary loop and connecting Class I lines have an operating history that demonstrates the inherent operating stability characteristics of the design. This includes a low susceptibility of cracking failure from the effects of corrosion (e.g., intergranular stress corrosion cracking). This operating history totals over 400 reactor years, including five plants each having over 15 years of operation and 15 other i
plants each with over 10 years of operation.
The 1978, the United States Nuclear Regulatory Commission (USNRC) formed the second Pipe Crack Study Group. (The first Pipe Crack Study Group established in 1975 addressed cracking in boiling water reactors cnly.) One of the objectives of the second Pipe Crack Study Group (PCSG) was to include a review of the potential for stress corrosion cracking in Pressurized Water Reactors (PWR's). The results of the study performed by the PCSG were presented in NUREG-0531 (Reference 6-1) entitled " Investigation and Evaluation of Stress Corrosion Cracking in Piping of Light Water Reactor Plants." In that report the PCSG stated:
"The PCSG has determined that the potential for stress corrosion cracking in PWR primary system piping is extremely low because the ingredients that produce IGSCC are not all present. The use of hydrazine additives and a hydrogen overpressure limit the oxygen in the coolant to very low levels.
Other impurities that might cause stress-corrosion cracking, such as halides or caustic, are also rigidly controlled. Only for brief periods during reactor shutdown when the coolant is exposed to the air and during the subsequent startup are conditions even marginally capable of producing stress-corrosion cracking in the primary systems of PWRs. Operating experience in PWRs supports this determination. To date, no stress-corrosion cracking has been reported in the primary piping or safe ends of any PWR."
6-1
During 1979, several instances of cracking in PWR feedwater piping led to the establishment of the third PCSG. The investigations of the PCSG reported in NUREG-0691 (Reference 6-2) further confirmed that no occurrences of IGSCC have been reported for PWR primary coolant systems.
As stated above, for the Westinghouse plants there is no history of cracking failure in the reactor coolant system loop or connecting Class 1 piping. The discussion below further qualifies the PCSG's findings.
For stress corrosion cracking (SCC) to occur in piping, the following three conditions must exist simultaneously: high tensile stresses, susceptible material, and a corrosive environment. Since some residual stresses and some degree of material susceptibility exist in any stainless steel piping, the potential for stress corrosion is minimized by properly selecting a material immune to SCC as well as preventing the occurrence of a corrosive environment. The material specifications consider compatibility with the system's operating environment (both internal and external) as well as other material in the system, applicable ASME Code rules, fracture toughness, welding, fabrication, and processing.
The elements of a water environment known to increase the susceptibility of austenitic stainless steel to stress corrosion are: oxygen, fluorides, chlorides, hydroxides, hydrogen peroxide, and reduced forms of sulfur (e.g.,
sulfides, sulfites, and thionates). Strict pipe cleaning standards prior to operation and careful control of water chemistry during plant operation are used to prevent the occurrence of a corrosive environment. Prior to being put into service, the piping is cleaned internally and externally. During flushes and preoperational testing, water chemistry is controlled in accordance with written specifications. Requirements on chlorides, fluorides, conductivity, and pH are included in the acceptance criteria for the piping.
During plant operation, the reactor coolant water chemistry is monitored and maintained within very specific limits. Contaminant concentrations are kept below the thresholds known to be conducive to stress corrosion cracking with 6-2
the major water chemistry control standards being included in the plant operating procedures as a condition for plant operation. For example, during normal power operation, oxygen concentration in the RCS and connecting Class 1 lines is expected to be in the ppb range by controlling charging flow chemistry and maintaining hydrogen in the reactor coolant at specified concentrations. Halogen concentrations are also stringently controlled by maintaining concentrations of chlorides and fluorides within the specified limits. This is assured by controlling charging flow chemistry. Thus during plant operation, the likelihood of stress corrosion cracking is minimized.
6-3
SECTION 7 CONSIDERATION OF PUMP VIBRATIONS Piping vibrations are known to occur in systems with active pumps. The magnitude of these vibrations in 2 inch and larger Class 1 piping is such that there have been no instances of failures in operating PWR plants due to pump induced vibrations. Failures in non-Class 1 piping have occurred but these are not related to the criteria for postulation of breaks in Class 1 piping.
These failures occurred outside cor.tainmerit in the vicinity of positive displacement charging pumps in the chemical volume and control system.
All of the break locations on South Texas Project that would be deleted by use of CUF = 0.4 criteria are located within the containment building and limited to 2 inch line size or larger. In addition STP uses centrifugal charging pumps for normal operations.
For 2 inch and larger Class 1 piping (such as that being covered in this CUF criteria for the South Texas Project), vibrations are induced by the reactor coolant pump. A series of calculations were carried out to determine the driving force parameter, Kg , as a function of the flaw depth using the accumulator piping system described in Sections 2 and 3. This stress intensity factor is then compared to the threshold stress intensity factor for fatigue crack growth in stainless steel. The results show that vibrations induced by the reactor coolant pump do not significantly affect the calculated fatigue crack growth even for moderate size flaws.
7.1 Estimate of Fatigue Threshold Stress Intensity Range The air environment threshold stress intensity ranges (AKth) f 304 stainless steel are listed in Table 7-1. To our knowledge, there are no th data in pressurized water at 600*F. However, with a proper analysis AK of the existing air environment AK results, a conservative value of th AK th in pressurized water may be estimated.
7-1
th in dry air at 75'F is smaller than that in In Table 7-1, the value of AK laboratory air. This behavior is due to oxide-induced crack closure (Refer-ences 7-1 through 7-3). During near-threshold fatigue crack propagation, oxide deposifs are often observed in moisture-containing environments. The formation of oxide debris is believed to result from fretting oxidation (References 7-1 through 7-4). Moreover, the thickness of oxide deposits have been measured to be comparable to the crack tip opening displacement. These sizable oxide deposits in wet environments will wedge the crack tip. They also promote the crack closure level, which in turn decreases the effective stress intensity range (AK,ff = K,,, - Kelosure, where K,,, and K are the maximum and closure stress intensities, respectively).
elosure This wedging action results in slower crack growth rates and higher AK th' as compared to the data in dry environments.
As the test temperature increases, thermal oxidation occurs and a thick oxide layer will form on the fracture surface. These oxide deposits further promote oxide-induced crack closure, thereby giving a higher AK th value with increasing temperature, as shown in Table 7-1. The values in Table 7-1 were taken from the work of Usami (Reference 7-5), which is presented in Figure 7-1.
The presence of pressurized water may have two effects on near-threshold crack growth behavior; (a) increases oxide thickness and thus oxide-induced crack closure and (b) introduces hydrogen enhancement of growth. Due to the lower yield strength of 304 stainless steel, the influence of hydrogen in enhancing growth may not be significant. This conclusion is supported by the findings of Bamford (Reference 3-2) that the PWR water environment did not significantly affect growth rates above the threshold region. Therefore, oxide-induced crack closure is likely to be the dominant effect from the environment. Recent research on Type 403 stainless steel confirm the above statementz, i.e., AK th f 403 steel in water is larger than that in air due to oxide-induced crack closure (Reference 7-6).
Therefore, in Type 304 stainless steel, the value of AK th in pressurized water at 600'F is estimated to be greater than the 572'F air results of 6.0 ksi/in as seen in Table 7-1 (Reference 7-5). There is a difference of 7-2
approximately 2 ksi /in for AK th in dry and laboratory air environment. It is estimated that the value of aK th in pressurized water at 600*F is about 7 j ac.e 7.2 Calculation of Stress Intensity Factors for Vibrating Loads The vibratory loads on the accumulator lines will result in a strets intensity factor which is a function of the flaw size. To calculate the applied stress intensity factor, the expression of Raju and Newman (Reference 7-7) was used.
Stress intensity factors were obtained for both inside and outside surface i flaws, and can be expressed by the general form, 0.5 3 K y = (y) G3 (a/c, a/t, t/R, d) Aj a5 (7-1) where a/c: Aspect Ratio a/t: Ratio of crack depth to thickness of a cylinder t/R: Ratio of thickness to inside radius
- Crack front location in degree w/2 2
2 Q1/2 = / (cos e + sin2,)1/2 do o
G 3 = Influence functions for inside or outside surface flaws.
A j = Coefficients of polynominal representation of stress distribution, as shown for example in Eq. 3-2.
7.3 Stress Limits From Vibratory Monitoring The South Texas Units 1 and 2 piping systems will be monitored during hot functional testing to ensure that the vibratory limits of OM3 (Reference 7-8) will be met. This requires that the vibratory stresses in the pipe be limited 7-3
to the alternating stress value for stainless steel at 10 11 cycles, from Figure I.9.2.2 of Section III of the ASME Code (Reference 7-9). This implies that the alterating stress in an as-welded butt joint should be limited to about 7.5 ksi.
7.4 Interaction of Flaw Size, Alternating Stress and Stress Intensity Factor In the Vibratory Range Calculations using the stress intensity factor expression described in Section 7.2 were carried out for a range of loadings applied to the accumulator piping geometry. The goal of this work was to determine what combination of alternating stress and flaw depth would produce a stress intensity factor equal to the threshold value developed in Section 7.1.
For the calculations, the stress was assumed to be uniform through the wall at the location of the postulated flaw. Then a series of values of alternating stresses were assumed, and stress intensity factors were calculated at a range of flaw depths. Flaws were postulated at both the inside surface and outside surface of the pipe wall.
Only the alternating stresses from vibrations were considered, even though the accumulator line will have other loads, for example internal pressure. These additional loads would be added to the minimum as well as the maximum values of stress, and thus would not change the range of stress intensity factor AK. Only the R ratio (KImin/KImax) would change, but the effect of R ratio has already been maximized in the development of the reference threshold stress intensity.
The results of the calculations show that a flaw with a depth of at least
[ ]a,c.e percent of the wall thickness would be required to produce a stress intensity factor which exceeds the threshold of [ Ja,c.e when subjected to an alternating stress intensity of 7.5 ksi. For smaller stress ranges, much larger flaw depths would be required, as may be seen from Figure 7-2.
7-4
Another way o' looking at the data is provided in Figure 7-3. This figure presents the results for an inside surface flaw of three different depths, in terms of the relationship between alternating stress and the range of stress intensity fao' tor AK. Here it may be seen that for a postulated flaw [
Ja c.e of the wall thickness, even the maximum allowable alternating stress (7.5 ksi) leads to a stress intensity factor range of [
j a,c.e Therefore it may be concluded that the example accumulator line has a large tolerance for vibratory loads, and such loads will not impact the integrity of the line. Similar conclusions would be reached for other lines, because the only difference from one line to another would be the wall thickness and pipe diameter.
7.5 Comparison of the Alternating Stress of 7.5 ksi with Plant Measurements As part of the hot functional testing of some of the more recent Westinghouse type nuclear power plants, accelerometers are placed at various locations on the primary loop piping system. From the vibration measurements so obtained, an analysis is performed which converts the measurements into stresses.
Re:ent acceserometer measurements during the hot functional testing of two typical four-loop plants were examined. For both plants, the maximum displacement observed was less than [ la,c.e For one plant the maximum vibratory stress in the reactor coolant piping due to normal operating conditions was found to be less than [ la.c.e; in the other, less than
( 3a,c.e ,
Accelerometers were not placed on the accumulator lines during hot functional testing for the two plants in question. However accelerometers were placed at the center of some of the cold leg spans. The displacements were conservatively summed by the root mean square method and the resulting displacement was used in a simpi.' beam analysis to obtain an alternating stress. The stress so obtained was less than [ Ja,c.e ,
7-5
1 It is thus seen that the calculated vibratory stress for the accumulator line is almost a factor of [ la,c.e less than the threshold alternating stress of 7.5 ksi. A factor of'at least ( la,c.e exists for the primary loop itself. Also from Figure 7-2 it is seen that at the alternating stress level of [ Ja c.e ksi, the threshold ak of ( Ja c.e g, not violated for any crack depth calculated.
7-6
TABLE 7-1 VALUES OF AK th FROM USAMI (Reference 7-5)
TEMPERATURE AK th ENVIRONMENT (*F) (ksi / in)
Dry Air 75 2.8 Laboratory Air 75 4.6 Laboratory Air 572 6.0 Laboratory Air 1022 8.0
)
7-7
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- 4 sso t. Alt, M
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Figure 7-1: Threshold Fatigue Crack Growth Data for 304 Stainless Steel 7-8
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i e
Figure 7-2: Relationship between Alternating Stress and Postulated Flaw Depth at which the Threshold Stress Intensity Range is[ ]a,c.e 8
7-9
a.c.e
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Figure 7-3: Relationship between the Range of Stress Intensity Factor and the Alternating Stress for Postulated Flaws in an Example Piping System 7-10
SECTION 8 USE OF C INDICES IN FATIGUE CRACK GROWTH ANALYSIS In FCG calculations, a stress distribution is applied to a selected flaw and the growth of the crack is calculated for the history of the loadings. These stress distributions can be obtained by simplified calculations or finite element analysis. When obtaining stresses by simplified methods, a stress index is applied to a nominally calculated stress (M/Z). This stress index is based upon testing, finite element analyses or other forms of detailed calculation. For Class 1 piping these indices are provided in Subsection NB (Reference 8-1) for typical nuclear piping components. Three types of stress indices are defined, B, C, and K indices. The B index reflects the strength of a component to withstand sustained loadings and is tied to a limit capacity; thus, it has no bearing on the FCG calculation. The K index is a factor to account for small surface defects which are already included in the FCG calculation. The C index reflects the actual distribution of through-wall membrane plus bending stress intensity and therefore must be considered.
Three types of C indices exist one for pressure (C ), ne f r m ment 1
(C2 ), and one for thermal discontinuity (C ). In general the C indices 3
must be considered in the FCG analysis. However, for the FCG analysis typically required on a PWR Class I syttem, it will be demonstrated that an index of 1.0 is reasonable for C y, C2 and C3.
In PWR Class 1 piping the most probable location for a small flaw to exist is in a girth butt weld which cannot be visually examined on the inside surface (except on primary coolant piping). Two other possible cases are longitudinal welds which are not used on Class 1 piping at the South Texas Project and socket welds. The break postulating criteria for socket welds are not being changed for the South Texas Project.
At the girth butt welds there are several configurations which could exist:
- 1) Girth butt weld in straight pipe
- 2) Girth butt welds at elbows
- 3) Girth butt welds at valve / equipment nozzles.
8-1
When evaluating girth butt welds for FCG, it is the axial stresses which are controlling. This is important because the C indices do not deal with only the axial stress and ins'tead are associated with the stress intensity which could be controlled by a hoop stress. For the components listed above published reports and finite element analysis completed by Westinghouse provide sufficient information to evaluate the effect of the discontinuity on the axial stress.
For the girth butt weld in straight pipe, the C indices are not required since a " gross" discontinuity does not exist, which is consistent with the codes indices of 1.0.
For the girth butt weld at an elbow, there is some affect of the curved pipe at the weld location. Based on Reference 8-2, the C2 index is based primarily upon circumferential stresses. The amplification of axial stresses is much less than circumferential (about 1/2). Further the axial stresses at ,
the weld are only slightly higher than the nominal stresses.
Considering these factors leads one to the conclusion that the butt weld at an elbow is essentially the same as a butt weld in straight pipe for axial stresses. This, in fact, was the conclusion drawn from the Marki fatigue tests (Reference 8-3) and is the current Code methodology. Therefore the use of a C index of 1.0 at a girth butt weld is acceptable for FCG 2
calculation. For pressure stress (C )1 a similar argument would lead to the same conclusion and for thermal transients3(C ) n significant discontinuity exists and therefore is not a concern.
Girth butt welds of valves and equipment nozzles are normally referred to as tapered-transition-joints. Axial stresses due to pressure and moment loadings are very similar and will be discussed together. Figure 8-1 illustrates the stress distribution at a typical tapered transition joint (a: found at South Texas Project) resulting from applied axial load. This distribution has been noted in several finite element analyses and is very similar to the effect of longitudinal pressure stress or bending moment on a pipe. As can be seen from 8-2
the distribution at the discontinuity, an axial tensile load causes a compressive stress on the inside surface, which subtracts from the average, and a tensile stress on the outside surface. Since tensile stresses drive crack growth, using the nominal stress distribution, which corresponds to C 2
= 1.0, is conservative for a tapered transition joint. For thermal transient effects using a C3 index of 1.0 is generally conservative for the tapered transition joints encountered in the South Texas Project Class 1 piping.
In conclusion the use of nominal stress equations is acceptable for the applications of FCG considered in the South Texas Project Class 1 piping. In general however, C indices must be considered in the determination of stresses for FCG analysis.
8-3
~
8,C e W
FIGURE 8-1 STRESS DISTRIBUTION AT A TAPERED TRANSITION JOINT DUE TO AN AX1AL L 8-4
SECTION 9 DISCUSSION AND CONCLUSIONS Houston Lighting and Power Company has proposed to the Nuclear Regulatory Commission that the cumulative usage factor screening criterion for break postulation in the South Texas Project Units 1 and 2 nuclear plants be set at 0.4 rather than the value of 0.1 which is currently applied. The value of 0.4 is consistent with the proposal of the American Nuclear Society Working Group on Pipe Break. Increasing the value to 0.4 eliminates the need for around
[ Ja,c e pipe whip restraints and jet impingement barriers at the South Texas Project plants. This would result in considerably less congestion inside the containment building and a significant reduction in rean-rems over j
the life of the plant. Overall plant safety is judged to be increased since '
the fatigue lives of the piping systems involved have been shown to continue to exhibit large margins compared to service life. Also the cost savings over the life of the plants are significant. It is demonstrated in this report that extremely large margins exist for crack extension by fatigue even for an i enveloping piping system (a typical accumulator line) with a CUF of
[ ja,c.e ,
A fatigue crack growth analysis at the worst location based on the stresses (static and cyclic) and geometry is first performed for the enveloping accumulator line. In depth technical details of the analysis are presented.
Applicable transients are identified and stress analysis procedures are outlined. The appropriate stresses for a fatigue analysis at the worst location are presented.
The procedure for calculating fatigue crack growth is outlined and the applicable fatigue crack growth law is presented. An initial small flaw was evaluated for fatigue crack growth for over fifty reactor lifetimes (over 2000 years). Very large margins against a crack growing to significant size are demonstrated. For example, for the flaw to grow to [ ]a c.e through the 9-1
wall requires over [ ]a,c.e [
]a,c.e wall penetration occurs at near [
]a,c.e phile [ la.c.e penetration is shown to occur at around [ ]a,c.e ,
In order to assess the margins in other piping lines, the procedure for calculating the CUF is reviewed. It is then shown that CUF is essentially a comparative measure of fatigue crack growth for the piping lines for which a 0.4 CUF criterion is proposed. Thus the results for the accumulator line with a CUF of [ Ja,c.e illustrate ample margin for such lines. The large margins shown for the CUF of [ Ja,c e for the accumulator lines show that conservatisms exist using a CUF of 0.4 as a screening criteria for break postulation.
Experience with cracks occurring in Westinghouse type PWRs is presented.
Intergranular stress corrosion cracking (IGSCC) is shown not to be of concern. Additional mechanisms for crack appearance and propagation do not exist.
The potential for vibratory stresses to enhance fatigue crack growth is examined. A threshold stress intensity range for fatigue crack growth at 600'F is shown to be around ( Ja ,c.e The allowable vibratory alternating stress is 7.5 ksi based on ASME Code Section III procedures and OM3 procedures (Reference 7-8). For the alternating stress of 7.5 ksi, a flaw would have to be at least [ ]a,c.e of the wall thickness to exceed the threshold stress intensity factor. An initial flaw [
Ja,c.e of the wall thickness leads to a stress intensity factor of less than [ ]C (less than half the threshold value) for the maximum alternating stress of 7.5 ksi.
The application of C indices in fatigue crack growth analysis is discussed.
It is shown that the use of nominal stress equations (i.e., the indices are 1) is acceptable for the FCG analyses considered in the South Texas Project Class 1 piping.
9-2
Displacements obtained from accelerometers on primary piping during recent hot functional testing of two typical four-loop reactor plants were examined. The maximum stregs due to vibratory displacements was found to be less than [
Ja,c.e For the accumulator line, the estimated vibratory stress is seen to be less than [ Ja,c.e . In general, the vibratory stresses are seen to be much less than the allowable alternating stress (7.5 ksi).
The major conclusion of this report is that, for the case at hand, increasing the CUF to 0.4 does not significantly reduce the structural safety margins inherent in a CUF of 0.1. Thus the technical demonstration has been presented for the acceptance of the proposed 0.4 CUF screening criterion.
l l
9-3
SECTION 10 REFERENCES 1-1 USNRC Standard Review Plan, NUREG-0800.
1-2 Simonen, F. A. and Goodrich, C. W., " Parametric Calculations of Fatigue Crack Growth in Piping", NUREG/CR-3059, March 1983.
2-1 WECAN - Westinghouse Electric Computer Analysis, User's Manual - Volumes I, II, III,' and IV, Westinghouse R&D Center, Pittsburgh, PA, Third Edition, 1982.
3-1 McGowan, J. J. and Raymund, M., " Stress Intensity Factor Solutions for Internal Longitudinal Semi-Elliptical Surface Flaws in a Cylinder Under Arbitrary Loadings", Fracture Mechanics ASTM STP 677, 1979, pp. 365-380.
3-1 Bamford, W. H., " Fatigue Crack Growth of Stainless Steel Reactor Coolant Piping in a Pressurized Water Reactor Environment", ASME Trans. Journal of Pressure Vessel Technology, February 1979.
4-1 ASME B&PV Code Division 1,Section III, 1983 Edition.
5-1[
a,c,e 5-2 Swamy, S.A., et al, Technical Bases for Eliminating Pressurizer Surge Line Ruptures as the Structural Design Basis for South Texas Project, WCAP-10489, Westinghouse Electric Corporation, February 1984 (Westinghouse Proprietary Class 2).
l l
l 10-1
5-3 Swamy, S. A., Witt, F. J., Bamford, W. H., Additional Information in Suppcet of the Elimination of Postulated Pipe Ruptures in the Pressurizer Surge Lines of South Texas Project Units 1 and 2, WCAP-11256, WestMnghouse Electric Corporation, September 1986, (Westinghouse Proprietary Class 2).
6-1 Investigation and Evaluation of Stress-Corrosion Cracking in Piping of Light Water Reactor Plants, NUREG-0531, U.S. Nuclear Regulatory Commission, February 1979.
6-2 Investigation and Evaluation of Cracking Incidents in Piping in Pressurized Water Reactors, NUREG-0691, U.S. Nuclear Regulatory Commission, September 1980.
7-1 Suresh, S., Zamiski, G. F., and Ritchie, R. O., Met. Trans. A,12A,1981,
- p. 1435.
7-2 Liaw, P. K., Leax, T. R., Williams, R. S. and Peck, M. G., Acta Met., 30, 1983, p. 2071.
7-3 Liaw, P. K., Leax, T. R., Williams, R. S. and Peck, M. G., Met. Trans. A, 13A, 1982, p. 1607.
7-4 Benoit, D., Namdar-Irani, R. and Tixier, R., Materials Sci. and Eng., 45 i 1980, p. 1.
7-5 Usami, S., Fukuda, Y, and Shirda, S., " Micro-Crack Initiation and Propagation in Elevated Temperature Inelastic Fatigue", (to be published in ASME Transactions).
7-6 Personal Communications, P. K. Liaw, Westinghouse R&D.
7-7 Raju, I.S., and Newman, J.S., " Stress Intensity Factor Influence Coefficients for Internal and External Surface Cracks in Cylindrical Vessels" in Aspects of Fracture Mechanics in Pressure Vessels and Piping, ASME publication PVP Vol. 48, 1982.
10-2
7-8 Requirements for Preoperational and Initial Start-up Vibration Testing of Nuclear Power Plant Piping Systems ANSI /ASME OM3-1982, the American Society of Mechanical Engineers.
7-9 ASME Boiler and Pressure Vessel Code, Division 1, Section 3, 1983 Edition.
8-1 ASME Boiler and Pressure Vessel Code, Division 1,Section III -
Subsection NB, 1977 Edition.
8-2 Rodabaugh, E. C., Iskander, S. K., and Moore, S. E. , "End Effects on Elbows Subjected to Moment Loadings," March 1978, ORNL/SUB-2913/7.
8-3 Markl, A.R.C., " Fatigue Tests of Piping Components," Trans. ASME, Vol.
74, 1952.
i 10-3
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