ML12181A440

From kanterella
Jump to navigation Jump to search
Riverkeeper Pre-filed Evidentiary Hearing Exhibit RIV000118, Checworkstm Steam/Feedwater Application, Guidelines for Plant Modeling and Evaluation of Component Inspection Data, 1009599, Final Report, September 2004, IPECPROP00000271, at p.6
ML12181A440
Person / Time
Site: Indian Point  Entergy icon.png
Issue date: 06/29/2012
From: Gwaltney R, Alonzo Richardson, Server W, Yahr G
EG&G Idaho, Oak Ridge
To:
Atomic Safety and Licensing Board Panel
SECY RAS
Shared Package
ML12181A438 List:
References
RAS 22867, 50-247-LR, 50-286-LR, ASLBP 07-858-03-LR-BD01
Download: ML12181A440 (29)
v • d • e


Text

RIV000118 Submitted: June 29, 2012

        • -***'"** ./.-----.. *--*---~- - '

CASE STUDY OF THE PROPAGATION OF A SMALL FLAW UNDER torJr <?wo72~- 1i PWR LOADING CONDITIONS AND COMPARISON WITH THE ASME CODE DESIGN LIFE COMPARISON OF ASME CODE SECTIONS III AND XI*

G. T. Yahr and R. c. Gwaltney Oak Ridge National Laboratory Oak Ridge, Tennessee CONF-860722--12 Ao K. Richardson and W. L. Server EG&G Idaho, Inc. TI86 005150 Idaho Falls, Idaho ABSTRACT A cooperative study was performed by EG&G Idaho, Inc., and Oak Ridge National Laboratory to investigate the degree of con-servatism and consistency in the AS~ Boite~ and P~essu~e Ves-set Code Sect. III fatigue evaluation procedure and Sect. XI flaw acceptance standards. A single, realistic, sample problem was analyzed to determine the significance of certain points of criticism made of an earlier parametric study by staff members of the Division of Engineering Standards of the Nuclear Regula-tory Commission. The problem was based on a semielliptical flaw located on the inside surface of the hot-leg piping at the reactor vessel safe-end weld for the Zion 1 pressurized-water reactor (PWR). Two main criteria were used in selecting the problem; first, it should be a straight pipe to minimize the computational expense; second, it should exhibit as high a cumulative usage factor as possible. Although the problem se-lect~d has one of the highest cumulative usage factors of any straight pipe in the primary system of PWRs, it is still very low.

The Code Sect. III fatigue usage factor was only 0.00046, assuming it was in the as-welded condition, and fatigue crack-growth analyses predicted negligible crack growth during the 40-year design life. When the analyses were extended past the design life, the usage factor was less than 1.0 when* the flaw had propagated to failure. The current study shows that the criticism of the earlier report should not detract from the conclusion that if a component experiences a high level of cy-clic stress corresponding to a fatigue usage factor near 1.0, very small cracks can propagate to unacceptable sizes.

  • Research sponsored by the Office of Nuclear Regulatory Research, u.s. Nuclear Regulatory Commission under Interagency Agreement No.

40-550-75 with the U.S. Department of Energy under Contract No.

DE-AC05-840R21400 with Martin Marietta Energy Systems~ Inc.

By accoptan::o ol thlt~ a**tl~l!l, th~: fll!bilHI1af or recipient acknowlcdgtJs thll U.S. Gc'l:;rnmurn's riGht to r~t~in a n 011

  • e;-. :lu!~ivc, rn*,~ft**.t _ frl"'n.

ficcn:-_.C' in ~nd ~J ~ * .......

~: !":Oi::/* ight c:o*4*crin.:."! !:~~

ortic!c-.

', .. 1. INTRODUCTION The fatigue design approach of Sect. III of the AS~ Boite~ and P~essu~e Vessel Codel is based on the experimentally determined relation-ship between elastically calculated stress range and fatigue life.2 Fa-tigue damage accumulated by the component at different stress ranges is accounted for by lineat'ly adding the fraction of life consumed at each stress range. This cumulative usage factor is not allowed to exceed unity.

Section XI of the ASME Boite~ and Pressu~e Vessel Code3 includes a procedure that allows continued operation after defects are found during inservice inspection by using a fatigue crack-growth analysis to demon-strate that the defect will not propagate to a critical size prior to the next inspection. Because this procedure is, in essence, a fundamentally diff~rent fatigue design approach from the cumulative usage factor ap-proach of Sect. III, it is natural that the consistency of the two ap-proaches, which will actually be applied to the same component, would be questioned. More importantly, indications of possible defects below cer-tain sizes are not a cauGe for rejection under Sect. III.Section XI al-lows defects of certain sizes without requiring reanalysis. A logical question that arises is whether those acceptable defect indications always meet the requirements of Sect. XI when they are found after the component has been placed in service.

In NUREG-0726 (Ref. 4), a simplified analysis was done to calculate

'the magnitude of acceptable crack sizes consistent with the maximum fa-tigue usage allowed by the ASME Code. This analysis indicated that tf a component experiences a high level of cyclic stress corresponding to a usage factor of 1.0, very small cracks can propagate to sizes that exceed acceptance criteria. This work received considerable criticism by indus-try. The principal criticisms were concerned with the simplifications employed in the analysis, which were recognized by the authors when the analysis was done.

As a result of the work reported in Ref. 4, staff members in the Di-vision of Engineering Standards [now identified as the Division of Engi-neering Technology (DET)] of the Nuclear Regulatory Commission (NRC) be-came concerned about the consistency and relationship between the fatigue design curves in Sect. III, crack-growth curves in Sect. XI, and the de-fect acceptance standards in Sects. III at.d XI of the AS~ Boiler and P~essu~e Vessel Code. Therefore, the present study was initiated to de-termine whether these concerns are justified and whether some restric-tions may be necessary when predicting the fatigue life of a flawed com-ponent. The present study was not designed to be a sufficient basis for recommending Code changes; it was intended to determine the validity of specific points of criticism of the earlier study by examining a realis-tic component.

The fatigue rules for Class 1 components in Sect. III of the ASME Code use S-N curves derived from data that were obtained from polished 1/4-in.-diam specimens and Miner's linear damage hypothesis. The flaw evaluation procedures of Sect. XI of the Code use linear-elastic fracture mechar.ics (LEFM) to predict the growth of existing flaws under cycling loading. Undetectable flaws and manufacturing defects sometimes exist in components. It is re~sonable to suppose that such cracklike defects will propagate under cyclic loading if the stress range is high enough. For consistency, use of the Sect. XI LEFM procedures should not predict crack growth of expected flaws to critical size when the rules of Sect. III are satisfied. Howevec, the simple and preliminary analyses of NUREG-0726 indicate that very small cracks can propagate to sizes that exceed the critical flaw size and cause failure if the crack area experiences a

usage factor close to unity. Thus, there is concern that the fatigue de-sign requirements of Sect. III and the crack acceptance standards of Sect. XI might need to be changed. Therefore, a more detailed study was undertaken to determine whether changes are needed in Sects. III and XI to ensure conservatism and consistency.

DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi-bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer-ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

2. PROBLEM DESCRIPTION An actual reactor component was analy?.ed to ensure that the conclu-sions of NUREG-0726 (Ref. 4) are relevant because much of the criticism was that a realistic load histogram was not used. A simple geometry was chosen to avoid unnecessary analytical complexity. Furthermore, the problem was selected on the basis of having a relatively high usage factor. The highest usage factor in the primary coolant system of a P,ressurized-water reactor (PWR) is generally at the terminal end of the ho~-leg pipe. Usage factors as high as 0.95 have been calculated at that location,s and the problem was selected on the basis of that reference.

Although it was later discovered that current designs result in much lower usage factors at this location, the study was continued because higher usage factors were found only in complex geometries such as noz-zles and elbows of PWR primary systems.

The plant chosen to serve as the basis for the present study is Westinghouse's PWR Zion-1 reactor. This particular plant was chosen be-

' cause necessary information on loading, including thermal transients, is available in the open literature 6 , 7 and because the pipe is not clad.

The location is the terminal end of the hot-leg piping where it is *welded to the "safe end," which is attached to the outlet nozzle of the reactor vessel. The nominal inside diameter of the pipe is 29 in., and the nomi-nal wall thickness ls 2.5 in. *rhe hot-leg pipe was manufactured out of SA-376 type 316 stainless steel material.

To evaluate the conservatism of Sect. XI acceptance standards, an analysis of fatigue crack-growth effects on a defect that was just ac-ceptable by both the Sects. III and XI standards was desired. Since the DET wanted potentially the worst case, a surface flaw was chosen because of the higher stress-intensity factor for the same size flaw.Section III acceptance limits [NB-2540 (Ref. 8)] allow surface linear indications with dimensions less than 3/16 in. and internal elongated indications of 3/4-in. length for thicknesses greater than 2-1/4 in. The size of this surface indication is so small that any flaw depth with an aspect ratio less than 0.5 is easily acceptable under Sect. XI (IWB-3514). Therefore, two approaches to a flaw model were used.

1. The first approach (which was chosen by the DET as the overall model to be used) uses the 3/16-in. length specified in Sect. Ill for actual surface linear indications. A flaw depth of 0.050 in. was chosen based upon a radiography detection limit of a depth of 2% of the wall thickness. The corresponding aspect ratio a/i, of 0.267, is consistent with the aspect ratios of flaws generally found in service.9 If the eventual crack-growth analyses prove conservative, this particular flaw wilL not prove anything meaningful about the Sect. XI acceptance limits.
2. The other approach uses the Sect. XI flaw characterization ap-proach that treats an internal (subsurface) indication near the surface as if it were a surface flaw. It is assumed that crack growth will im-mediately cause an internal defect to penetrate to the surface. Using the 3/4-in. allowable length i from Sect. III for an internal indication, critical defect depths can be determined by use of the ASME Sect. XI acceptance standards for preservice and inservice inspection (Table IWB-3514-2). Flaw aspect ratios a/i of 0.288 and 0.366 are obtained,

dictating depths of 0.216 and 0.2745 in. for preservice and inservice inspection, respectively.

The service loads for Zion-1 were obtained from Refs. 6 and 7. Vi-bration loading is not normally included in the service loads considered in the fatigue evaluation of PWR components and was not included in the service loads conside<ed in Refs. 6 and 7. A study of PWR cold-leg piping integrity at Battelle Columbus LaboratorieslO showed that vibra-tion loading could make an important contribution to fatigue crack growth. In the absence of appropriate data on levels of vibration of the hot legs in PWRs, the values assumed by the Battelle investigators for vibration in the cold legs of PWRs were also assumed in the present study. The assumed vibration stress variation of 1000-psi range at a frequency of 1000 cycles/min could result from pipe vibrations caused by such things as flow-in~uced vibration. The events considered and the number of times they occur are given in Table 1. The loads during each transient are given in Table 2. ~e-ma~~um stress campeaeRts at the in etde-and-uotstde surfaces ate-g~ for ea~~~~s{~t in Table 3a The-1:tt-t'S§f raRges at"8 gi\0~-tttt:l.-e dt, amtJPe unit his to grams are given in Table=')'. The selection of the unit hisfograms is critical to a crack propagation analysis. Extreme cycles early in the histogram may propa-gate the crack sufficiently so that subsequent moderate cycles will cause additional crack propagation. If those same moderate cycles had been ap-plied first, the crack would have propagated less. Standard histograms have been developed in the aerospace industry based on many years of flight data, but this concept has not been developed for nuclear plants.

The unit histograms in Table3J{were arrived at by uniformly distributing all transients over the plant life. Because all the postulated cycles for the various transients are not convenient, even, multiples of the startup/shutdown transient, it was necessary to devise a method to dis-tribute the "odd" traP"'ients uniformly during the plant life. Therefore, the three different blocks were devised to simplify the computations.

The first block included only the five most frequent events; the second included those plus five other less frequent events; and the third in-cluded only the Safe Shutdown Earthquake (SSE). This same approach was used in the cold-leg integrity evaluation at Battelle. lO

Table 1. Zion-1 events Transient Event Number of events a, b Startup/shutdown 500 c, d Plant loading/plant unloading 15,000 e, f Step increase/step decrease 2,000 g Reactor trip and recover at 400 startup 1 Loss of flow and abnormal 80 loss of load m Loss of secondary pressure 5 h Hydrotest to 3125 psig, 400°F 10 OBE Operating basis earthquake 200 SSE Safe shutdown earthquake 1 Vi b. Vibrations 2.1 X 1010 Table 2. Load transients for hot-leg pipe based on Zion-1 Delta temperature Pressure Bending momenta Transient through wall (psig) (in.-lb) (oF) a, b 2235 1. 22 X 10 7 19 c, d 110 (50/480) 24 e, f 220 (20/480) 12 g 510 (90/480) 117 1 550 (120/480) 190 m 2235 (301/480) 410 h 3125 (330/480) 19 OBE 2.77 X 107 SSE 2.82 X 10 'J asource of moments - Startup/shutdown: This is for a temperature change from 70 to 550°F. For other tran-sients, a fraction of this is used based on the ratio of temperature changes in the transients to 480°F (e.g.,

Transient c, d).

3. CODE SECTION III FATIGUE DESIGN APPROACH 3.1 Background The fatigue design approach of Sect. Ill (Refs. 1, 11, 12) of the ASME Boite~ and P~essu~e Vessel Code for less than 10 6 cycles is based on concepts deve: , ~d by Langer2 on the basis of the Manson-Coffin 1 3, 14 relationship bet~o_P.< plastic strain amplitude and fatigue life. The re-lationship between plastic strain amplitude and fatigue life has been es-tablished by extensive strain-control push-pull fatigue testing of smooth 1/4-in.-diam, unflawed, hourglass *shape specimens. The design curves of ASME Code Sect. III are based on a best-fit curve drawn through the test data that has been lowered by a factor of either 2 on stress or 20 on cy-cles, whichever is more conservative at each point. At cyclic lives be-low about 4 x 10 3 cycles, the factor of 20 on cycles is the controlling factor so that the factor of safety on stress in this low-cycle regime is more than 2. At cyclic lives above about 4 x 10 4 cycles, the factor of 2 on stress is the controlling factor and the factor of safety on cyclic life is more than 20.

Reference 15 cites five specific things that are accounted for by the factor of 2 on stress: surface finish, size, material variability, environment, and residual stress. Other things that are not accounted for by the factor of 2 on stress, which must therefore be allowed for in the design and analysis, include stress concentration, corrosion, and metallurgical notch effects caused by differences in the weld and base metal.

Testsll, 16 on prototypic welded pressure vessels and piping with girth butt weldsl 7 have generally demonstrated that the design curves ob-tained using the factors of 2 and 20 are adequate. Some of the tests on 6-in. pipes with girth butt welds 1 8 included welds that had an inten-tional defect, that is, a lack of penetration produced by not completing a l-in. section of root pass. Although their lives were less than those of similar pipes without intentional defects, their lives were longer than predicted by the Code Sect. III fatigue design procedure.

A large number of fatigue tests were carried out by Harrison and Maddoxl9 on near full-size pressure vessels. Harrison and Maddox com-pared the results from these tests with fatigue design curves of the ASME Code Sects. III and VIII and the B~itish VesseL Code BS-5500. Compari-sons between the design curves and the test results were made for the following regions: at the toes of nozzle welds, at nozzle welds failing under circumferential stress loading, in the main seam welds, in repair welds, and in parent metaL In each of these regions, failures occurred below the S-N curves given in the ASME Code and, in some cases, below the S-N curves given in BS-5500.*

  • These results have drawn a reaction from the ASME Code Committee; it has drafted a letter to Dr. Harrison citing two basic errors in Harrison and Maddox's application of the ASME Code rules. The letter states that correct evaluation of the data will show the Code rules to be significantly more conservative than the paper indicates.

The fatigue curves of ASME Code Sect. III are logarithmic plots of stress-intensity amplitude S vs number of cycles to failure N. The ex-perimental data were actually based on strain-control tests, and the stress values used for plotting the data were determined by multiplying by the modulus of elasticity. The actual stresses were considerably lower than these fictitious stresses in the low-cycle regime (<10~ cy-cles) where considerable plasticity occurs. However, this fictitious stress has the advantage of being directly comparable to elastically cal-culated stresses.

More recently, the high-cycle regime has received increased atten-tion,20,21 and the fatigue curves for austenitic stainless steel that previously stopped at 106 cycles have been extended to 1011 cycles. Be-cause of the need to distinguish between load-controlled and strain-controlled cycling and to account for mean stress effects in the very high cycle regime, three curves are provided in the Code for fatigue de-sign for lives above 106 cycles and are shown in Fig. 1 (Refs. 15, 22).

Curve A is an extension of the low-cycle Code S-N curve for (106 cycles using the original Langer equation. Curve B corresponds to the original fatigue design curve at 10° cycles and to one-half of the average fatigue stress amplitude for annealed stainless steel under load-controlled cy-cling beyond 10'l cycles. 23 Curve C was obtained from the stress-controlled data curve adjusted for the maximum effect of mean stresses that can be retained during cycling. A flow chart is given in the Code for determining which of the three curves should be used.

Miner's linear damage theory2 4 is used for determining the cumula-tive damage from different load cycles. A fatigue usage factor is cal-culated by summing the ratios of the number of cycles expected to the number of allowable cycles determined from the S-N curve for all the stress cycles that are postulated to occur. The fatigue damage is taken ORNL-DWG 84-6108 ETD 30 28 26

'\'r-.. .__

! 24 \
  • u; CURVE A rn"'
u. 22

\.

0 Vl

~~

UJ 20

J

...J 18

<1: r--- CURVE B 16 ........

14

~"---- buRJE d I

tad 109 N, NUMBER OF CYCLES NOTE:

E = 28.3 X 106 psi Fig. 1. ASME Code Sect. III high-cycle design fatigue curves for austenitic steels, nickel-chromium-iron alloy, nickel-iron-chromium alloy, and nickel-copper alloy for temperatures not exceeding 800°F (from Ref.

22).

q-Table fl* Stress indices used in fatigue stress calculation*

Internal pressure Moment loading Thet'lllal loading Case Description cl Kl c2 K2 c3 K3 1 Straight pipe 1.0 1.0 1.0 1.0 1.0 1.0 2 Flush weld 1.0 1.1 1.0 1. 1 0.6 1.1 3 As-welded 1.0 1.2 1.0 1.8 0.6 1.7 4 Highest possible 1.0 5.0 1.0 5.0 1.0 5.0 stress concentration 5 Stress concentration 1.0 2.5 1.0 2.5 1.0 2.5 for crack 6 Stress concentration 1.0 2.75 1.0 2.75 0.6 2.75 for crack and flush weld 5

Table ~. Number of lifetimes required to produce usage factor of 1.0 Case Number of lifetimes Straight pipe 13,000 Flush weld 8,100 As-welded 2,200 Highest SCF 14 Cracka SCF 310 Cracka SCF and flush weld 201 aA 0.050-in.-deep by 3/16-in.-

long semielliptical surface crack.

II as ?ero for stress cycles that are less than the allowable stress at 1011 cycles. Rodabaugh and Wright 25 have demonstrated the application of the Code Sect. III fatigue evaluation procedures to nuclear piping systems.

3.2 Results Loads and stress ranges were derived for the terminal end of the Zion-1 hot-leg piping on the basis of the data in Refs. 6 and 7 al'l:a ~

..gioert;o:;Ln....Ia.::S.leooooea The thermal stresses iziF4?sl!lle (j aFe ....*lfa~~d on* the tem-perature distributions given in Ref. 26. A

~~e fatigue evaluation procedure used is given in Sect. III of the Code. Equations (10) and (11) of Ref. 27 were used in the fatigue analysis of the hot-leg pipe./

Six different fatigue analyses were performed using Sect. III27 pro-cedures. In the first, it was assumed that the area of interest was away from the weld and no fatigue strength reduction factors were used. In the second it was assumed that the area was a flush weld; in the third analysis, it was assumed that the area was in an as-welded condition; in the fourth analysis, the maximum fatigue strength reduction factor as specified in the Code30 was applied to the peak stresses; and in the fifth analysis, the stress concentration effect of the flaw that is as-sumed to exist was taken into consideration. The fatigue reduction fac-tor for a short crack 0.05 in. deep is 2.5 according to Langer.3l The sixth analysis was based on a combination of the second analysis (flush weld) and the fifth analysis (stress concentration factor for a crack),

which was developed by multiplying these two stress indices together.

The stress indices used fot these six analyses are given in Table4jl'. ~

-restJlts ef the ....fatigue aRalyses are gi vee in~eleta 9 14. The fatigue analyses gave very low usage factors, and the number of lifetimes re-quired to produce a usage factor of 1.0 for each case is given in Table

~~. As can be seen, the calculated lifetimes for the fatigue analyses vary from 13,000 for the straight pipe to 14 for the highest possible stress concentration case.

4. FATIGUE CRACK-GROWTH ANALYSIS Section XI of the ASME Boile~ and P~essu~e Vessel Code3 provides ac-ceptance standards for defects found during inservice inspections. For no defects or defects with a size.less than the specified acceptance levels, the Code does not require any remedial action; the component is considered acceptable. For defect sizes larger than the acceptance levels, an evaluation using fracture mechanics (taking into account the factors discussed in nonmandatory Appendix A of Sect. XI) can be per-formed to show whether crack growth will cause failure before the next inspection or end-of-life. If this analysis is successful, the component fs conditionally acceptable, and no repair or replacement is required.

However, an upgraded inspection plan is specified to monitor any future crack growth.

The criteria in Sect. XI for acceptance of flaw indications without evaluation (for ferritic st<:els with no1ninal yield strength below 50,000 psi) were based on nrovisions for protect:ion against nonductile failure contained tn Appendix G of Sect.* Ill of t.he Code. 2 2 These pro-visions provided the basis for using a reference flaw of depth equal to 1/4 the wall thickness t and length Q equal to 1-1/2 times the thick-ness. As a measure of conservatism to establish an allowable acceptance limit for a surface flaw, the flaw depth a of 1/10 of that postulated in Appendix G of Sect. III was selected (i.e., aXI = aiii/10). Fracture mechanics stress-intensity factor solutions from Appendix G were then applied to determine equivalent surface and subsurface flaw size accep-tance limits for different flaw geometries. -FJ.gHns 2 and 3 (taken from Ref. 32) Hhtetr~te tl\e appFoael\ and rem~lts for surfaee (F~. 2) and sYbsurfaee (Fig. 3) flaws. St1bst1rfaee f}aw sizes can be larger, as-sMWf'-

....~n~t~.---

iA Figa 3, due to lower stress-intensity faetoF valt1es for-equ4:-v-a1e

~

For austenitic steel piping, application of LEFM is not suitable for fracture analysis due to the fully plastic conditions that are often de-veloped for this highly ductile material prior to fracture. As a conser-vative basis for the development of acceptance standards for austenitic steels, a net-section ductile yielding criterion was initially used taking advantage of the high strain hardening of austenitic steels. Although the permissible flaw sizes derived (using the net-section yielding ap-proach) are conservative for strain hardening materials, the standards for acceptance of flaw indications without evaluation were even more con-servatively lowered to correspond to the range of flaw sizes detectable by presently used ultrasonic techniques. *Ffgure-=4 illustrates tM=s 'ii

--=fereuce beLweeli the ('ermi!lsf<),la flaw sizes ~=net: !leetioll-ryield

_approae'R ....ana tfle Fange of al lowa.We inai~~

ahilit) tl\resfie¥a. For consistency with the ferritic steel acceptance standards, a flaw with an aspect ratio a/Q of 1/6 was .taken as the nor-malizing point in defining the ultrasonic detectability threshold.

The inservice extension of flaws may be estimated by a fatigue crack-growth analysis. Development of this analysis is dependent on knowledge of the flaw size, applied stresses, and an appropriate stress-intensity factor solution. Two analytical procedures for calculating the stress intensity factor are the ASME BaiZe~ and P~essu~e Vessel Code Sect. XI*

Appendix A approach and a more refined solution based on influence func-tion techniques.33 The following discussion summarizes fatigue crack-growth behavior and the estimated crack-growth response based on the two stress-iniensity factor solutions.

4.1 Fatigue Crack-Growth Behavior Fatigue crack propagation behavior can generally be described by a power law in the Paris or stage II region of crack propagation. This power law relates the incremental fatigue crack-gro>rth rate da/dN to the stress-intensity factor range 6K in the following manner:

m I da/dN =C (6K) , (?a)

J3 or I

log da/dN = log C + m log ~K , <lb) where C and m are experimentally determined constants.

Variations in the cyclic stress-intensity factor ratio R * ~inl~ax are accounted for through the use of an effective stress-intensity factor

/<;: z.

value Keff* Substitution of Keff for 6K in Eq. (i&J gives Eq. 07), which relates crack-growth rate to effective applied stress-intensity factor range and includes the effects of the cycle sttass ratio:

Keff is defined in the Walker relationship3~ as 3

K eff

.. --=--

ilK (1 _ R)n

<p) or in the Rabbe-Lieurade relationship35 as ilK 4-Keff = (1 - R/a) ' <1>

where a and n are material-dependent parameters" Other variables such as environment, cyclic frequency, stress-intensity threshold, residual stresses, and crack retardation may affect the fatigue crack propagation behavior depending on the material and existing conditions.

4.2 Section XI Analysis For a Sect. XI Appendix A analysis, a stress-intensity factor K1 is defined as:

.5 (l<()

where (J = membrane and bending stresses, respectively; m' ab Mm, Mb = membrane and bending free surface correction factors32 for a flat plate, respectively; a .. flaw depth for a surface flaw, Q flaw shape parameter.

Membrane and bending stresses are determined from the linearization of the actual through-wall axial stress profile as specified in Sect. XI Appendix A of the Code. The linearization technique defines two stresses (at the outside surface and depth of a surface flaw) and uses these.posi-tions in determ.ining an equivalent linear representation of stress dis-tribution. Parameters Q, ~, and Mb are determined from Appendix A curves that are considered to be conservative.32 A stress-intensity range is defined as G.

(-tt)

This range is substituted into the fatigue crack-growth law and integrated to give a change in flaw size ~a for a corresponding number of fatigue cycles ~N.

4.3 Computer Code Analysis The Electric Power Research Institute (EPRI) computer code DRIVE was developed to calculate stress-intensity factors *for surface cracks in pipes by use of influence functions.33 Modifications in the computer code to incorporate fatigue crack-growth laws allow a more accurate cal-culation of the crack-growth response than the Sect. XI approach, because the conservatism of tha free surface corrections for plates is elimi-nated. The free surface correction factors adjust the basic values of the stress-intensity factors to account for finite thickness and flaw location effects.

4.4 Material Considerations i

The effect of various parameters on the fatigue crack propagation behavior of a 316 stainless steel weld defect needs to'be considered to complete a fatigue crack-growth analysis. Applicable fatigue crack-growth data and parameters such as environment, frequency, stress-intensity factor threshold, residual stresses, and crack retardation were investi-gated.

4.4.1 Crack-growth data The fatigue crack-growth analysis of a 316 stainless steel weld de-fect requires compilation of fatigue crack-growth data in a PWR environ-ment. A data base of crack-growth results for 316 stainless steel product forms in air and PWR environments was compiled with assistance from the Battelle/EPRI data base management system, EDEAc.36 Fatigue crack propa-gation rates for 316 stainless steels differ from those of other aus-tenitic stainless steels under similar conditions;37 therefore, only 316 stainless steel plate, casting, and weldment data were utilized. Figure ft G

ORNL-DWG 84-6112 ETD SYMBOL MATERIAL ENVIRONMENT 0 316ss AIR D

AIR

  • c. 316 CASTING PWR 316 WELDMENT AIR
  • PWR 10-?L-------------~--------~----~----~--~--~~--~

10 100 Keff* EFFECTIVE STRESS INTENSITY FACTOR 2--

Fig. J* Compiled fatigue crack-growth data for 316 stainless steel.

shows weldment, casting, and plate data separated by material form.3B-40 Growth rates in austenitic stainless steel weldments are generally equiva-lent to or lowe~ than growth rates in wrought stainless steels; therefore, all 316 stainless steel product forms were included in the analyzed data base.41 A statistical 1_regression was performed to determine the parame-ters C and m of Eq. (~}. Figurez7* also shows a graphical upper bound to the data and its corresponding C and m parameters.

The fatigue crack-growth rate data are plotted as a function of Keff in Fig.z~. As described in Sect. 4.1, Keff is a function of the stress-intensity factor 6K and the cyclic stress ratio R. Whether defined as in Eq .3$ (Walker) or Eq .4ri (Rabbe-Lieurade), negligible differences occur be~ween the two methods of calculating Keff for small R ratios (0 ( R <

0.2). The R ratios of the compiled 316 stainless steel data ~re to (0.2; thus, one plot (Fig.Z,O of da/dN vs Keff was utilized for the data, where Keff was in the form of a Walker relationship.

/6 4.4.2 Other fat.igue crack propagation parameters A variety of parameters affect the fatigue crack propagation rates of austenitic stainless steels. These parameters include environment, frequency, stress intensity threshold, residual stresses, and crack re-taraation.

Temperature and environment can have a profound effect on fatigue crack growth. As mentioned previously, both air and PWR environments were included in the data base. Reference 41 indicated a negligible dif-ference between air and PWR environment. The temperature range chosen was 500 to 800°F, which encompasses the reactor operating temperature of 550°F and is conservative. The effect of frequency has been assumed to be negligible at these temperatures.41 A large number of cycles at very low stresses can result in crack growth to a critical flaw size within the design life of the reactor if there is no stress-intensity factor threshold. For this reason, calcula-tions boU1 include..\j and excluded a stress-intensity factor threshold as shown in Tables~~ £1=(Sect. 4.7). A threshold value for 316 stainless steel welds in a PWR environment has not yet been determin~d, but there are published values for stainless steels in air environments.9,10, 42 Threshold value6 of 4.6 ksi*lin7 and 2.6 ksi*lin. were utilized in the calculations.

Residual stresses were ignored in this st~dy. There are currently no generally accepted means for taking crack retardation into account.

Crack retardation occurs when a high cyclic stress blunts the crack tip and causes less crack growth to occur until the crack grows out of the blunted crack stress field. Ignoring crack retardation will be conser-vative, and this approach was taken in the analyses.

4.5 Thermal and Stress Analyses In a crack-growth analysis, a stress-intensity factor range 6K must be calculated as indicated in Sect. 4.2. This calculation is dependent on an existing time-dependent axial stress distribution for each of the transients presented earlier. This time dependence is primarily due to the thermal stress component of the total axial stress distribution.

A thermal analysis was first performed to determine the temperature gradients for the hot-leg pipe location of concern for all transients considered.26 Most of the input data for the Zion-1 hot-leg came from Refs. 6 and 9; in some cases, the graphical fluid temperature data in Ref. 9 did not agree with tabulated data in Ref. 6, probably because of typographical errors.

The radial temperature gradient results were then analyzed to allow calculation of axial thermal stress distributions through the pipe wall assuming no end restraint. 4 3 One-dimensional temperature distributions for various times in each transient were generated; with the maximum dead weight, thermal expansion, and pressure stresses determined in Ref. 6, the total axial stress distributions as a function of time were deter-mined ** ~J,...~s an t!'K&Hif'!e of t:he tGote:l sh*ass gN.Ueau stdt:fa=--

,_.{Qgj:ut Hmes=4'm: 'funsi:ez:t i!, f "fa:h~ An LEFM approach was applied

I ,.

7 tJl!P to all transients, including Transient m where the maximum stre3s at the inside surface exceeded yield.

4.6 Critical Flaw Size To determine if fatigue would cause failure of the flawed section, a failure criterion based on limit load was applied. The criterion was based on the new Appendix C to the ASME Code.44 A critical flaw depth to thickness ratio a/t is determined as a function of flaw length to pipe circumference and applied stress conditions. Thus, as the flaw grows in length, the critical a/t can change. The margin of safety for mlflawed piping is maintained in this approach for the section of the pipe reduced by the flaw area (net section area); the critical crack depth is also never allowed to exceed 75% of the wall thickness.

4.7 Results of Crack-Growth Analyses Two approaches were taken to calculate the crack growth response of the hot-leg safe-end weld defect. The first approach closely follows the guidelines of Appendix A Sect. XI of the ASME Boile~ and P~essu~e Vessei Code, while the second approach utilizes more current methodolo-gies and mean material properties.

4.7.1 Section XI analyses For the most severe stress distribution as a function of time for each transient, the actual stress distribution is approximated using the linearization technique illustrat*ed in Appendix A Sect. XI of the Code.

Membrane and bending stresses are determined from the linearized stress distribution, and stress ranges ~crm and ~ob are determined based on the assumption that the transients occur during steady state operation (with the exception of the hydrostatic.test). Parameters~' Mb, and Q along with ~om and ~crb are functions of the crack depth and are calculated for each cycle to determine an updated ~K. This ~K range is substituted into the Rabbe-Lieurade relationship or Walker relationship, along with the conservative upper-bound crack growth constants C and m, and integrated for an increase in flaw size for a given number of cycles 6N. The spec-

. trum of loading is the same as that for the Sect. III fatigue analysis.

Two approaches based on the calculated values of Mm and Mb were used in the Sect. XI Appendix A analyses. The first assumed a constant aspect ratio (a/2c), while the second allowed the aspect ratio to vary. Mb is defined for the depth dimension <a = 0°) and length dimension <a = 90°),

while ~is only defined in the depth dimension. Thus, assuming a con-*

stant aspect ratio eliminates the need for a correction factor in the length dimension. Assigning ~ a value of one in the length dimension allows separate calculations of flaw growth in the depth and length dimensions.

The calculated crack-growth r~~onses of the two hot-leg safe-end weld defects are shown in Table~J~~~* Analyses were conducted for the

c_,

Table ~ Number of 40-year lifetimes until critical fbw size for Sect, Ul allowable flaw (a

  • 0.050 in.) (Sect. XI analysis)

Stress- Critical a Critical b intensity Number of Criticalc flaw flaw factor 40-year *spect depth length threshold lifetimes ratio (in.} (in.)

(ksi*/iii':")

Constant aspect ratio Walker relationship 4.6 316 1.87S 7.03 0.267 Raboe-Lieurade relationship 4.6 331 1.87S 7.03 0.267 2.6 328 1.883 7.06 0.267 None 2 1.87S 7.03 0.267 Variable aspect ratio Walker relationship 4.6 ISS 1. 229 17.0 0.072 Rabbe-l.ieurade relationship 4.6 181 1. 521 14.21 0.107 2.6 173 0.511 39.62 0.013 None 0.85 0.600 33.11 0.018 alnitial flaw depth 0.050 in.

binit1a1 flaw length O.J87S in.

alnitial aspect ratio 0.267 in.

Table 7.}-9'. Number of 40-year lifetimes until critical flaw size for Sect. XI allowable preservice flaw (a

  • 0.216 in.} (Sect. XI analyses)

Stress- Critical a Criticalb Criticalc intensity Number of flaw flaw factor 40-year aspect depth length threshold lifetimes ratio (in.) (in.)

( ksi* /iri":")

Constant aspect ratio Walker relationship 4.6 104 1.875 6.511 0.288 Rabbe-Lieurade relationship 4.6 109 1. 875 6.512 0.288 None 0.55 1.877 6.517 0.288 Variable aspect ratio Walker relationship 4.6 33 1.238 16.90 0.073 Ra bbe- Lt eur ade relationship 4.6 40 1. 549 14.171 0.109 None 0.12 o. 726 25.73 0.028 alnitial flaw depth 0.2i6 in.

binitta: flaw length 0.75 in.

cinitial aspect rat to 0. 288 in.

!7 surface flaw model decided on by the DET (a

  • 0.050 in.). for a larger preservice internal (subsurface) indication treated as a surface flaw (a
  • 0.216 in.), and for a still larger internal (subsurface) indication treated as a surface flaw (a R 0.2745 in.). Results for the inservice flaw are not given in the tables. Results for all three cracks are shown in Fig~l. Identification of the type of relationship (Rabbe-Lieurade or Walker) and the stress-intensity threshold are given for each calcu-lation along with the final flaw depth. length,. and aspect ratio *

. IPl 'Fa=l51?ie itl a~ the Sec1:-::?KI=1!i=R'", ts era g!cetr fot calcaletieus ac:

-e~ i:lifl8l flew sh~~~ttestog1P 1Het:ime. For the DET suggested flaw, negligible crack growth occurred for all calculations except for those that excluded a stress-intensity factor threshold. When the aspect ratio was allowed to vary and the stress-intensity factor threshold was excluded, the smaller flaw reached a critical flaw size prior to the end of the 40-year design Hfetime. For the larger pre-service flaw model (a = 0. 216 in.), a similar result was obtained in which negligible crack growth occurred for all calculations except those that excluded a stress-intensity factor threshold.

ORNL-DWG 84-6114 ETO USAGE FACTOR 0.018 0.0005 0.005 0.015 0.05 0.083 0.5 1.0 10 I

I I I g

r /

I I 1-ll.

LU

/

I 0

(.)

<(

I cr

(.)

.; I 0.1 /

,/

  • -*-*-*-*-* -------*~

- - - - DEEPER INSERVICE CRACK (a= 0.2745 in.)

---DEEPER PRESERVICE CRACK (a= 0.216 in.)

  • -*-ALLOWABLE SECTION Ill CRACK (a= 0.050 in.)

0.01 ~-------:'::-------~-------:-:::-1:-::-------1 1 10 100 1000 5 000 40-YEAR DESIGN LIFETIMES Fi~/.(. Crack depth determined using Sect. XI analysis as function of 40-year design lifetimes and usage factor.

Crack-growth response as a function* 'of 40-year design lifetimes was calculated for the two flaw models discussed previously. The number of 40-year design lifetimes until a critical flaw size is reached is shown in Tables~~ and7~. Additional calculations using a Rabbe-Lieurade re-lationship and a 4.6-ksi*fin7 stress-intensity factor threshold were made for a Sect. XI allowable inservice indication (a

  • 0.2745 in.).

Thirty-four design lifetimes were needed before a critical flaw depth of 1.54 in. was obtained for the inservice indication.

In the Sect. III fatigue analyses, 2188 lifetimes were required to give a usage factor of one for the as-welded condition. Assuming a usage factor of one denotes failure,* a "critical usage factor," which is the ratio of the calculated number of lifetimes to 2188, can be assigned to each of the flaw sizes. Figure~\ shows crack growth determined using the Rabbe-Lieurade relationship 'and a variable aspect ratio in a Sect. XI analysis as a function of both 40-year design lifetimes and usage fac-tor. Critical usage. factors of 0.015, 0.018, and 0.083 correspond to the deeper inservice flaw (a= 0.2745 in.), deeper preservice flaw (a

  • 0.216 in.), and the shallow flaw (a= 0.050 in.), respectively. Note that there is only a small difference between the results for the preser-vice and inservice flaws. Therefore, tabular results were not given for the inservice crack. Both gave total lifetimes that were a fraction of the Sect. III fatigue life for this component in the as-welded condition.

4.7.2 Computer code analyses Crack-growth response was also calculated using the EPRI computer code DRIVE.33 This more refined analysis calculated stress-intensity factors for surface cracks in pipes using influence functions and the exact stress distribution for the highest ~K anytime in the transients.

Crack-growth rate constants C and m from the regression analyses were used for one set of calculations, and another set of calculations uti-lized the upper-bound constants for direct comparison with the Sect. XI analyses. Calculations of the final flaw size for a 40-year design life-time were determined using both the Walker and Rabbe-Lieurade relation-ships. The crack-growth response after a 40-year design lifetime was calculated for the two flaw sizes as shown in Tables"i? andet<r. The mean fatigue crack-growth analyses showed very little flaw growth as compared with the analyese using an upper-bound crack-growth law. Com-parisons made between the Sect

  • XI analyses and the DRIVE computer code analyses for similar conditions showed negligible difference and very little crack growth, although the Sec. XI analyses consistently showed greater growth in the length dimensions as compared with the computer code analyses.
  • In reality, failure would not be expected to occur until the usage factor exceeded one by some undefined margin. The Code fatigue design curves used in determining the usage factor were derived from fatigue test data from smooth specimens reduced by a factor of 20 on cycles or 2 on stress, whichever is greater. However, a summary of many tests on proto-typic vesselsl6 shows that the design fatigue curves are very realistic; that is, the actual design margin is usually much less than 20 on cycles.

Zl

<6" Table~. Computer code DRIVE analysis for Sect. III allowable flaw (a

  • 0.050 in.) for a 40-year design lifetime Stress- Finala Finalb intensity Finale flaw flaw factor aspect depth length threshold ratio (in.) (in.)

(ksi*/in':")

Upper-bound growth rate Walker relationship ~.6 0.0503 0.1878 0.268 Rabbe-Lieurade relationship 4.6 0.0502 0.1878 0.267 None 0.1316 0.3168 0.415 Mean growth rate Walker relationship 4.6 0.0500 0.1875 0.267 Rabbe-Lieurade relationship 4.6 0.0500 0.1875 0.267 None 0.0517 0.1895 0.273 12 Initial flaw depth 0.050 in.

lllnitial flaw length 0.1875 in.

elnitial aspect rat lo 0.267.

Table ~. Crack computer code DRIVE analyses for Sect. XI allowable preservice flaw (a

  • 0.216 in.) for a 40-year design lifetime Stress- Final a Finalb intensity Finale flaw flaw factor depth aspect length threshold (in.) (in.) ratio (kst*/Til.)

Upper bound growth rate Walker relationship 4.6 0.219 0.755 0.290 Rabbe-Lieurade relationship 4.6 o. 218 o. 754 0.289d None 1. 941 3.991 0.486 Mean growth rate Walker relationship 4.6 0.216 0.750 0.288 Rabbe-Lieurade relationship 4.6 o. 216 0.750 0.288 None 0.255 0.796 0.320 ainitial flaw depth 0.216 in.

binitial flaw length 0.75 in.

clnitial aspect ratio 0.288.

dFlaw reached critical size prior to end of 40-year design lifetime.

5. DISCUSSION The Sect. III fatigue analysis for the as-welded condition is the one that would be used by the designer when qualifying this component.

The fatigue usage factor was so low that 2200 lifetimes would be required to reach s fatigue usage factor of 1.0. The Sect. XI analysis predicted that a critical flaw size would not be reached until 150 to 330 lifetimes had been expended. Thus, in this case the Sect. III analysis would per-mit a longer period of operation than a Sect. XI analysis would. Both analyses include design margins, so failure would not be expected even after the allowable period. Relative margins are not known; thus, a clear and direct comparison of the two approaches is not possible. Note that when the stress concentration factor for the assumed flaw was used, the allowable number of lifetimes according to a Sect. III analysis was 310, which is very near the 316 and 321 lifetimes predicted when a Sect. XI

  • analysis was done, assuming a constant aspect ratio for the crack. Fur-thermore, when the stress concentration factor for the crack was super-imposed on the flush weld, the Sect. III analysis gave a prediction of 190 lifetimes, which is very near the predicted lifetimes of 155 and 181 given by the Sect. XI analysis when a variable aspect ratio was allowed.

Generally, the stress'levels were at the high-cycle end of the fa-tigue curve where the factor of 2 on stress was used to generate the de-sign curve from fatigue data. Higher stress levels would have resulted in so much plasticity that LEFM would not have been applicable. Because the crack initiation phase is a relatively high portion of the total life in high-cycle fatigue, the LEFM approach would be expected to be conser-vative if no cracklike defect happened to be present, since it ignores crack initiation. Even if an initial cracklike. defect should exist, some cycling will probably occur before propagation starts.

The earlier study4 by Anderson, Weidenhamer, and Johns concluded that if a. component experiences a high level of cyclic stress that corresponds to a usage factor of 1.0, very small cracks can propagate to sizes that exceed Code-specified limits. That study was the impetus for the current study. The current study is an attempt to answer the principal concerns expressed by the reviewers of Anderson's study. Those concerns were mostly a result of the simplifying assumptions that they used. The spe-cific concerns were

1. the through-the-wall stress distribution was not prototypic;
2. all the loading was assumed to occur at one stress level, which does not account for the variation in loading as demonstrated by operating time histories; and
3. there are very few actual cases in which a component is subjected to stress levels having a usage factor of 1.0.

We will discuss what the current study reveals about each of these con-cerns.

for design application. Further analytical studies to determine whether this is generally true and to more fully determine the effect of varia-tions in the threshold stress-intensity factor on calculated lifetimes of a variety of components would help in defining how much effort is justi-fied on precise experimental determination of threshold stress-intensity factors.

6. CONCLUSIONS This study shows that fatigue failure of the terminal end of the Zion-1 hot-leg piping is extremely unlikely according to both the S-N approach and the fatigue crack-growth approach. The only way to directly compare the two methods is to compare the number of lifetimes that the methods would allow. The fatigue crack-growth approach allows fewer lifetimes of operation than the S-N approach. However, direct comparison of the two approaches is not valid because the design margin included in both procedures is variable and hard to quantify. In the case of the S-N approach, a factor of 2 on stress or 20 on cycles, whichever is the most conservative, is applied to the best-fit curve through the data. This results in a factor on cycles much greater than 2G in the high-cycle re-gime and a factor on stress greater than 2 in the low-cycle regime. How-ever, tests on prototypic vessels have shown that the actual design mar-gin can be much less ,16 A realisti.c fatigue cr.ack-growth analysis was performed for one lifetime, but the analysis was not continued for addi-

' tional lifetimes. If this c:malysis had been continued for a sufficient number of lifetimes to cause the crack to propagate to failure, it would have provided some indication of the margin included in the Sect. XI procedure. As it is, this margin is unknown.

Until recently, the assumption of the Sect. III fatigue approach (stress ranges less than that which will produce failure in loG cycles need not be considered) was potentially unconserv.ative because very small stress ranges of sufficient frequency can contribute an appreciable amount of fatigue damage. The recent extension of the fatigue design curves for austenitic steels to lOll cycles will help to take care of this problem for austenitic materials. Work is under way to also extend the fatigue design curves for ferritic steels to a higher number of cycles as well.

The existence of a stress-intensity factor threshold was an important assumption in the crack-growth analyses that determines how well this approach treats small stress-range events. Exclusion of a threshold caused extensive or critical crack growth within the 40-year design life-time. Also, the analytical stress-intensity factor calculations in Appendix A, Sect. XI of the Code do not produce consistent results with the influence function approach in the DRIVE computer program.33 The Sect. XI approach predicts faster growth on the surface of a part-through crack than at the center, whereas the DRIVE predictions show faster growth at the center relative to the free surface. This inconsistency makes it difficult to exactly quantify the final flaw dimensions and the critical number of 40-year design lifetimes.

The current study is not a sufficient basis for defining any specific changes in either Sect. III or Sect. XI of the Code. However, a number of recent studies4,45,48, 49 have concluded that in certain instances the fatigue crack-growth approach is rrore conservative than the current Sect. III fatigue evaluation when initial flaws of a reasonable size are assumed. We suggest that it might be prudent to require that the fatigue crack-growth method be applied if the fatigue usage factor is very high.

Unfortunately, there is not sufficient information at this time to deter-mine what usage factor, if any, should trigger a requirement for a fatigue

crack-growth analysis. Explicit consideration of the existence of manu-facturing defects in the design Code would lead to a more reliable design for areas that a~tually experience high usage. Furthermore, since the potential manufacturing defect should be related to the method of manu-facture and level of inspection and quality control, there "~oUuld be .in-creased incentive to produce higher quality components where such quality is needed.

One direction that could be taken to improve the Sect. Ill fatigue design approach would be to require that a fatigue crack-growth analysis be done if the cumulative usage factor is higher than some designated value. The limited study by Anderson et al. suggests that for the problem that they examined and an initial crack depth of 5% of the wall thick-nesses, the fati~ue crack-growth approach would limit one to a cumulative usage factor of 0.3. However, considerable additional .work would be re-quired to determine the value of the cumulative usage factor when the fatigue crack-,growth approach predicted failure for a variety of problams before a definite value could be assigned to the designated cumulative usage factor that would trigger a fatigue crack-growth analysis. Such an approach would have minimum impact on the analyst applying the Code because very few locations would ever be expected to have a high enough cumulative usage factor to require the fatigue crack-growth analysis.

The "belt and suspenders" approach of requiring that both methods be used in those few critical locations would reduce the possibility of fatigue fa:r.lure.

Some additional work is needed to establish whether the stress dis-tribution in locations such as nozzles and elbows, where the fatigue usage factors are near 1.0, has an appreciable effect on the number of cycles required to cause a crack to propagate to failure. More importantly, documented fatigue failures in boiling water reactors (BWRs) and PWRs should b~ used as the basis for comparing the validity of the cumulative usage factor approach and the fatigue crack-growth approach.

This research suggests that the points of criticism of the earlier*

parametric study (NUREG-0726) concerning its lack of realism in the through-the-wall stress distribution and loading histogram should not have an appreciable effect on the results of that study. The other prin-cipal point of criticism that fatigue usage factors are generally much less than 1.0 was verified. However, it is still important that the fa-tigue design procedures of Sec~. III ensure that a permissible flaw could not propagate to failure in the few instances where high fatigue usage factors do occur. This study concludes that additional studies are war-ranted to establish the need for rodification of the current Sect. Ill fatigue design approach and to establish a basis for such improvements.

ACKNOWLEDGMENTS The authors wish to acknowledge the contributions of C. J. Pientka of EG&G Idaho, who assisted with the computer code DRIVE, and B. L.

Harris and K. H. Liebelt of EG&G Idaho, who conducted the thermal and stress analyses.

Thanks are also due to the Metal Properties Council Task Force on Crack Propagation Technology (D. P. Jones, chairman); the American Society ~f Mechanical Engineers (ASME) Subgroup on Fatigue Strength (W. J. O'Donnell, chairman); the ASME Sect. XI Subgroup on Evaluation Standards (S. Bush, chairman); and W. H. Cullen, R. R. Maccary, S. W.

Tagart, c. R. Brinkman J. G. Merkle, G. H. Weidenhamer, and F. Hill for their comments and assistance. Finally, we acknowledge the support and encouragement of W. F. Anderson, E. T. Baker, D. J. Guzy, and N. Miegel.

REFERENCES

1. ASMg BoiteP and PPessuPe Vesset Code, Secti~ III, NucteaP PoweP PZant Components, Division 1, American Society of Mechanical Engi-neers, New York, 1983.
2. B. F. Lan,ger, "Design of Pressure Vessels for Low-Cycle Fatigue,"

J. Basic Eng. 84(3), 389-402 (September 1962).

J. ASME BoiteP and PPessuPe Vesset Code,Section XI, Rutes fop InseP-vice Inspection of NucteaP PoweP Ptant Components, American Society of Mechanical En,gineers, New York, 1983.

4. W. F. Anderson, G. H. Weidenhamer, and E. C. Johns, PPetimina~

Anatys*is of the F:ffect of Fatigue Loading and C'Mck FPopagation on CPack Acceptance CPitePia fop NucteaP PoweP Ptant Components, NUREG-0726, U.S. Nuclear Regulatory Commission, April 1981.

5. Pipe BPeaks foP the LOCA Anatysis of the Westinghouse PPima~J Coot-ant Loop, WCAP-8172-A, Westinghouse Electric Corp., January 1975.
6. A. L. Chan, S. C. Lu, E. F. Rybicki, and D. J. Curtis, PPobabitity of Pipe Fro.ctur>e in the PT'imaPy Cootant Loop of a PWR Ftant; Votume 3: Nonseismic StPess Ana.tysis; .Load Combination PPogmm; PPoject I Finat RepoPt, NUREG/CR-2189, val. 3, UCID-18967, vol. 3, August 1981.
7. S. C. Lu, S. M. Ma, and R. A. Larder, PPobabitity of Pipe FPactuPe in the PPimaPy Cootant Loop of a PWR Ptant, Vot. 4:. Seismic Re-sponse Anatysis; Load Combination PPogmm; PPoject I Finat Reporl, NUREG/CR-2189, val. 4, UCID-18967, vol. 4, September 1981.
8. ASME BoiteP and PPessuPe VesseL Code, Sect1:on III, Article NB-2540 1980.

. 9. D. 0. Harris, E. Y. Lim, and D. D. Dedhia, PPobabitity of Pipe FPac-tuPe in the PT'imary Cootant Loop of a PWR Plant; Volume 5: PPoba-bitistic Fro.ctuPe Mechanics Anatysis; Load Combination PPogpam; Pr>oject I ,Final Reporl, NUREG/CR-2189, val. 5, UCID-18967, vol. 5, August 1981.

10. M. E. Mayfield et al., Cotd Leg IntegPity Evatuation, NUREG/CR-1319, U.S. Nuclear Regulatory Commission, February 1980.
11. CPitePia of the ASME BoiteP and PPessuPe Vesset Code foP Design by Anatysis in Sections III and VIII, Division 2, American Society of Mechanical Engineers, New York, 1969.
12. L. F. Coffin, Jr., et al., "Report of the ASME Boiler and Pressure Vessel Committee, Special Committee to Review Code Stress Basis, Task Group on Fatigue," Tmns. ASME, cT. ProessuM Vessel Techno!.

100, 24D-42 (May 1978).

13. J. Tavernelli and L. F. Coffin, "Experimental Support for Generalized Equation Predicting Low-Cycle Fatigue," J. Basic Eng., Tmns. ASME, 533-37 (December 1962).
14. s. S. Manson, "Thermal Stresses in Design- Part 19: Cyclic Ufe of Ductile Materials," Mach. Des., 139 (July 7, 1960).

IS. M. J. Manjoine and R. E. Tome, "Proposed Design Criteria for High Cycle Fatigue of Austenitic Stainless Steel," in ASME Intemational Conferoence on Advances in Life Proediction Methods, Albany, New York, April 18-20, 1983, New York, 1983.

16. C. W. Lawton, "High-Temperature Low-Cycle Fatigue: A Summary of Industry and Code Work," E~. Mech., 257-66 (June 1968).
17. E. c. Rodabaugh and s. E. Moore, Comparoisons of Test Data with Code Methods foro Fatigue Evaluation, ORNL-TM-3520, Union Carbide Corp.*

Nuclear Div., Oak Ridge Nat!. Lab., November 1971.

18. E. Kiss, J. D. Heald, and D. A. Hale, £ow-Cycle Fatigue of P'Y'ototype Piping, GEAP-10135, General Electric (San Jose), January 1970.
19. J. D. Harrison and S. J. Maddox, "Derivation of Design Rules for Pressure Vessels, Avoiding Failure by Fatigue in Welded Construc-tions," Welding Institute Seminar (October 1979).
20. C. E. Jaske and W. J. O'Donnell, "Fatigue Design Criteria for Pres-sure Vessel Alloys," J. P'Y'essuroe Vessel ~er..:h~zo7.* , Tro..:xns. ASt'.fE 99, 584-92, November 1977.
21. Discussion of Ref. 15, J. Proesauroe Vessel Technol., Tmns. ASME 100, 236-53, May 1978.
22. ASME Boiler> and Proessuroe Vessel Code,Section III, Rules foro Con-strouction of Nuclear> Power> Plant Components, Division 1 -Appendices, American Society of Mechanical Engineers, New York, 1983.
23. M. J. Manjoine and E. I. Landerman, "Techniques for Fatigue Testing and Extrapolation of Fatigue Life for Austenitic Stainless Steels,"

J. Test. Eval., JTEVA 10(3), 115-20, May 1982.

24. M. A. Miner, "Cumulative Damage in Fatigue," J. AppZ. Mech., Tmns.

ASME 67(12), A-159-A-164, September 1945.

25. W. B. Wright and E. C. Rodabaugh, "A Method of Computing Stress Range and Fatigue Damage in a Nuclear Piping System," Nuct,. Eng. Des. 22, 318-25 (1972).
26. K. H. Liebelt, The~at, Transients fo~ Fractu~e AnaLysis of Zion 1 PWR Primary Loop Hot Leg Piping, EG&G Idaho, Inc., Internal Techni-cal Report No. RE-A-82-080, December 1982.
27. AS~ Boit,e~ and Pressu~e Vessel, Code,Section III, Paragraph NB-3650, Analysis of Piping Products (1980).
28. AS~ Boit,e~ and Pressu~e Vessel, Code,Section III, Appendix I (1980).
29. G. E. Forsythe, M. A. Malcom, and C. B. Moler, Compute~ Methods fo~

Mathematical, Computations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1977.

30. ASME Boit,e~ and ~essu~e Vessel, Code,Section III, Paragraph NB-3222, Level A Service Limits, Subparagraph 4e(2), 1980.
31. B. L. Langer, AppLication qf St~ess-Concent~ation Facto~s. Bettis Technical Review, WAPD-BT-18, April 1960.
32. R. R. Maccary, Nondest~ctive Examination Acceptance ~anda~s, Technical, Basis and DeveLopment of Boite~ and Pressu~e Vessel, Code, ASME Section XI, Division 1, EPRI NP-1406-SR, May 1980.
33. D. Dedhia and D. O. Harris, St~ess Intensity FactoPS fDF Su~face C~acks in Pipes: A Compute~ Code fo~ EvaLuation by Use of Inftuence Functions, EPRI NP-2425, June 1982.
34. E. K. Walker, "An Effective Strain Concept for Crack Propagation and Fatigue Life with Specific Applications to Biaxial Stress Fatigue,"

P~oc. Ai~ Fo~ce Conf. Fatigue and ~ct~e of Ai~c~aft Bt~ct~es and Mate~at,s, Miami Beach, Fla, December 1>-18, 1969.

35. P. Rabbe and H. P. Lieurade, "Etude a l'Aide de la Mecanique de la Rupture d'e la Vitesse de Fissuration en Fatigue d'une Gamme Entendue d'Aciers," Memoi~es Scientifiques, Rev. Metat,t,u~gie, LXIX, No. 9, September 1972.
36. Data base for Environmental Crack Model Development, maintained for EPRI by Battelle-Columbus Laboratories.
37. L. A. James, "Fatigue-Crack Growth Correlations for Design and Analysis of Stainless Steel Components," Pressure Vessel and Piping Division of the ASME, 82-PVP-25.
38. L. A. James, "Fatigue-Crack Propagation in Austenitic Stainless Steels," At. Ene~gy Rev. 14(1), 37-86 (1976).
39. L. A. James, "The Effect of Elevated Temperature Upon the Fatigue-Crack Propagation Behavior of Two Austenitic Stainless Steels,"

IntePnational ConfePence on Mechanical BehavioP of MatePiats# 1st Kyoto~ 1971 PPoceedings, 3, 1972, pp. 341-52.

40. P. Shahinian, H. Smith, and J. Hawthorne, "Fatigue Crack Propagation in Stainless Steel Weldments at High Temperature," Welding Resea1'ch Supplement, 527-32 (1972).
41. W. Bamford, "Fatigue Crack Growth of Stainless Steel Piping in a Pressurized Water Reactor Environment," J. PPessupe Vessel Technol.

101, 7}-79 (1979).

42. A. Pickard, R. Ritchie, and J. F. Knott, "Fatigue Crack Propagation in a Type 316 Stainless Steel Weldment," Met. Technot. 2, 253-63 (1975).
43. B. L. Harris, letter to w. L. Server, BLH-15-82, "Stress Analysis of Primary Coolant Loop Piping for The.rmal Transients in a PWR Plant,"

December 14, 1982.

44. ASME BoileP and PPessuPe Vessel Code,Section XI, Non-Mandatcry Appendix C, "Evaluation of Flaws in Austenitic Piping," Passed by Main Committee on 5/5/83 also to appear in the Winter 1983 Addenda to Section XI.
45. F. A. Simonen and c. w. Goodrich, Pa1'amet1'ic Calculations of Fatigue C~ck CPowth in Piping, NUREG/CR-3059, PNL-4537, R5, March 1983.
46. J, J. Hamn, J. E. Roberts, J. C. Lowry, and R. w. Burge, Analytical RepoPt foP FZoPida Powe1' and Light Company, St. Lucie Plant Unit No. 2 Piping, CENC-1501, Combustion Engineering, Inc., February 1982.
47. K. Kussmaul, "Developments in Nuclear Pressure Vessel and Circuit Technology in the Federal Republic of Germany," pp. 1-28 in St1'UC-tu1'al Integ1'ity of Light WateP ReactoP Components, ed. L. E. Steele et al., Applied Sciences Publishers, 1981.
48. P. M. Scott, B. Tomkins, and A. J. E. Foreman, "Development of Engi-neering Codes of Practice for Corrosion Fatigue," ASME Paper No. 82-PVP-30 (June 1982); also J. of FPessuPe Vessel TechnoZ.~ Tnans. ASME 105(3), 255~2 August 1983.
49. Letter, Carl E. Jaske, Battelle, to James A. Horak, Oak Ridge Na-tional Laboratory, private communication (February 26, 1982).
Retrieved from "https://kanterella.com/w/index.php?title=ML12181A440&oldid=2461742"