ML20095C997

Draft Pressurized Thermal Shock Evaluation of Calvert Cliffs Unit 1 Nuclear Power Plant,Chapter 5:Probabilistic Fracture-Mechanics Analysis of Calvert Cliffs Unit 1 Sequences

ML20095C997
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Site:	Calvert Cliffs
Issue date:	07/27/1984
From:	OAK RIDGE NATIONAL LABORATORY
To:	NRC
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ML20095D000	List: ML20095C997
References
REF-GTECI-A-49, REF-GTECI-RV, TASK-A-49, TASK-OR NUDOCS 8408230191
Download: ML20095C997 (169)

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A PRESSURIZ.ED THERMAL SHOCK EVALUATION 0F THE CALVERT Q.lFFS UNIT 1 NUCLEAR POWER PLANT List of Chapters .

Chapter 1 Introduction Chapter 2 Calvert Cliffs Unit 1 Nuclear Power Plant System Description Chapter 3 Development of Overcooling Sequences for Calvert Cliffs Unit i Nuclear Power Plant Chapter 4 Thermal-Hydraulic Analysis of Potential Overcooling Transients Occurring at Calvert Cliffs Unit 1 Nuclear Power Plant Chapter 5 Probabilistic Fracture-Mechanics Analysis of Calvert Cliffs Unit 1 Sequences Chapter 6 Risk integration of Potential Calvert Cliffs Unit 1 Overcooling-Sequences Chapter 7 Sensitivity and Uncertainty Analysis Chapter 8 Summary and Conclusions 4

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5.0. PROBABiLiSTlC FRACTURE-MECHANICS ANALYS1S OF CALYERT Q.1FFS UNIT 1 SEQUENCES 5.1. Introduction 5.2. Description of Basic Problem 5.3. Calculational Models 5.3.1. Fracture-Mechanics Model 5.3.2. Stress-Analysis Model .

5.3.3. Thermal Analysis Model 5.3.4. Probabilistic Analysis Model 5.4. Flaw-Related Data for the Calvert Cliffs-1 Reactor Pressure Vessel 5.5. Results of Analysis 5.5.1. Types of Analyses Conducted 5.5.2. Conditional Probability of Vessel Fallure 5.5.3. Sensitivity Analysis 5.5.4 Effect of including WPS 5.5.5. Effect of Proposed Remedial Measures on P(F E) 5.5.5.1. Reduction in fluence rate 5.5.5.2. Annealing 5.5.5.3. Increasing temperature of HPl coolant l

Chapter 5 Appendices K. Contribution to P(FlE) of Flaws in the Circumferential Welds and in the Plate Segments L. Compilation of Results of Calvert Cliffs-1 Probabilistic Fracture-Mechanics Analysis u

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LIST OF FIGURES.

5.1. Cross section and developed view of plate-type PWR pressure vessel 5.2. Cross sections of Calvert Clif fs-1 pressure vessel and core showing locations of vessel welds in beltiIne region 5.3. Developed view of Inner surf ace of beltline region of Calvei-t Cliffs-1 pressure versel, showing locations of welds 5.4. Illustration of a method of selecting (Kg ,)

5.5. Critical-crack-depth curves for a typical postulated PTS transient

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5.6. OCA-P program logic 5.7. Graphic illustration of the error in P y, consistent with the criteria uped for establishing the number of vessels simulated (Nyy )

5.8. P(FlE) vs EFPY for Calvert Cliffs-1 postuiated PTS transients 5.9. Histogrm of percent of Ir.itiations vs crack depth for first initiation event (Calvert Clif fs-1 postulated transient No.

8.3; 32 EFPY) 5.10. Histogre of percent of f ailures vs time of failure (Calvert Clif fs-1 postulated transient No. 8.3; 32 EFPY) 5.11. Histogram of percent of total Initiations vs relative temperature at which initiations take place (Calvert Clif fs-1 postulated transient No. 8.3; 32 EFPY) 5.12. Histogram of percent of total arrest events vs relative temperature at which arrest events take place (Calvert Clif fs-1 postulated transient No. 8.3; 32 EFPY) 5.13. P, T and h vs t for Calvert Cliffs-1 postulated transient No. 8.3 5.14 Wali temperature vs a/w, t for Calvert Cliffs-1 postuiated transient No. 8.3 5.15. WalI temperature vs t, a/w for Calvert Cliffs-1 postuiated

2 transient No. 8.3 ,

5.16. Critical-crack-depth curves for Calvert Cliffs-1 postulated transient No. 8.3; 32 EFPY, weld 2-203A 5.17. Effect on P(FlE) for transient No. 8.2 of reducing fluence rate at 7 EFPY by f actors of 2, 4 and 8 5.18. Effect on.P(FIE) for transient No. 8.3 of reducing fluence rate at 7 EFPY by factors of 2, 4 and 8 0

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/ s LIST OF TABLES 5.1. Parameters simulated in OCA-P 5.2. Material properties, fluences and vol ur. ss used In the LEFM analysis of the Calvert Cliffs-1 reactor vessel 5.3. Summary of calculated values of P(FlE) for the Calvert Cliffs-1 postulated transients 5.4(A) Summary sheet of OCA-P output for Calvert Clif fs-1 postulated transient No. 2.1 5.4(B) Summary sheet of OCA-P output for Calvert Clifi..-1 postulated transient No. 2.4 5.4(C) Summary sheet of OCA-P output for Calvert Cliffs-1 postulated transient No. 8.2 5.4(D) Summary sheet of OCA-P output for Calvert Clif fs-1 postulated transient No. 8.3 5.5. Sensitivity of P(FlE) at 41 EFPY to le changes in the mean values of several of the simulated parameters 5.6. Ef fect of including WPS in calculation of P(FlE) at 32 EFPY 5.7. Benefit of remedial measures, P(FlE)wRM/P(FlE)w/oRM>

at 42 EFPY for dominant transients a

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C0-5.1 5.0 PROBABILISTIC FRACTURE-MECHANICS ANALYSIS OF

. CALVERT CLIFFS UNIT 1 SEQUENCES R. D. Cheverton Oak Ridge National Laboratory D. G. Ball Martin Marietta Energy Systems, Inc.

Computer Sciences Division 5.1 Introduction This chapter provides detailed information regarding the probabilistic fracture-mechanics analysis of the Calvert Cliffs-1 reactor vessel and discusses (1) the conditions necessary for failure (through-wall cracking) of a PWR pres-sure vessel as a result of a PTS transient,~(2) the fracture-mechanics models used for evaluating vessel integrity, and (3) the results of a probabilistic fracture-mechanics analysis of the Calvert Cliffs-1 reactor vessel .for PTS

-loading conditions. Supplementary information is included in Appendices K and L , as noted in this chapter.

5.2 Description of Basic Problem i

During a PTS transient in a pressurized-water reactor (PWR), the reactor pressure vessel is subjected to thermal shcck in the sense that thermal stresses are created in the vessel wall as a result of rapid removal of heat from its inner surface. The thermal stresses are superimposed on the pressure stresses with the result that the net stresses are positive (tensile) at and near the inner surface of the wall and are substantially lower and perhaps negative else-where, depending on the magnitude of the pressure stress. The concern over the high tensile stresses near the inner surface is that they result in high stress intensity factors (K ) yfor inner-surface flaws _ that may be present. To compound the matter, the reduced temperature associated with the thermal shock and radi-ation damage result in relatively low fracture-toughness values for the vessel

v CC-5.2 material, particularly near the inner surface. Thus, there is' a possibility of propagation of initially very shallow as well as deeper flaws, and the probability increases with time because of the time dependence of radiation-damage.

The positive gradient in temperature and the negative gradients in stress and fluence through the wall tend to provide a mechanism for crack arrest. Even so, if the crack is very long on the surface' and propagates deep enough,.the remaining vessel ligament will become plastic, and the vessel internal pressure will ultimately result'in rupture of the vessel. Thus, for each thermal tran-sient there will be a maximum pennissible pressure that is a function of the time that the vessel has been in operation.

Crack propagation may also be limited by a phenomenon referred to as warm prestressing (WPS), which has been demonstrated to some extent in the laboratory 1

with small specimens and also in a rather large, thick-walled cylinder during a thermal-shock experiment.2 In such cases, WPS simply refers to the inability cf a crack to initiate while K isy decreasing with time, that is, while the crack is closing. While this special situatiun is encountered during some -

specific overcooling accidents, caution must be exercised in taking credit for WPS because changes,in the pressure that affect little else can delay or elimi-nate the requisite conditions for WPS.

The area of the vessel of particular concern in the event of a PTS tran-sient is the so-called beltline region, that is, the area directly across from the core where (1) the radiation damage is the greatest, (2) the thermal shock could be severe, and (3) a rupture of the vessel could preclude flooding of the core. Whether or not a particular degree of rupture associated with a particu-lar transient could in fact preclude flooding of the core has not been determined but is under investigation. For the purpose of this report, it is sufficient to predict whether a flaw will propagate completely through the wall of the vessel.

L l

3 CC-5.3 The radiation-induced reduction in fracture toughness of the vessel mate-rial is a function of the fast-neutron fluence and the concentrations of copper (a_co;. aminant) and nickel (an alloying element). Furthermore, for the same values of fluence, copper and nickel, radiation damage tends to be greater in the welds that join the segments of the vessel than in the segments (basematerial). In most PWR vessels the highest concentrations of copper are found in the welds, and many of these welds have high concentrations of nickel as well. Thus, for some PWR vessels the welds are of primary concern. However, the much larger surface area of the segments may offset the difference in radia-tion damage between segments and welds, if the density of surface flaws in the segments is about the same as, or greater than,that for the welds.

The beltline region of reactor pressure vessels is fabricated using either forged-ring segments or rolled-plate segments. Vessels made with forgings have only circumferential welds, while plate-type vessels have both circumferential and axial welds, as shown in Fig. 5.1. For plate-type vessels with staggered F5..

axial welds and for which radiation damage is much more severe in the welds than in the base material, the final surface length of a propagating inner-surface axial flaw tends to be limited to the length of the axial weld in which it resides, that is, the height of the shell course. Furthermore, only that portion of a weld that is within the axial bounds of the core need be considered because of the steep attenuation of the fast-neutron flux, and thus radiation damage, beyond the fuel region.

If the chemistry in adjacent plate segments is about the same, the extended surface length of an axially oriented flaw in a plate segment is also limited by the height of the core but not by the height of a shell course.

Because of an azimuthal variation in the fast-neutron flux (see Fig. 5.1) and possibly in chemistry, the extended length of an initially short, circumfer-entially oriented flaw located in a circumferential weld or in a plate segment also tends to be limited.

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5 C0-5.5 The behavior of an assumed flaw can be predicted for a given transient using fracture-mechanics methods of analysis. In such an analysis the parameters and

-considerations involved are the size, shape, and orientation of the flaw; the thermal and pressure stresses resulting from a specific transient; the tempera-ture and fast-neutron fluence distributions throughout the vessel wall; the effect of fluence and material chemistry on radiation damage; a variety of material properties; and a comparison of the stress intensity factor (K y) assoc-iated with the tip of the flaw with the material's static crack-initiation and crack-arrest fracture-toughness values (K Ic and XIa). Each of these factors must be considered in the development of an appropriate analytical model for evaluating the integrity of a PWR vessel when subjected to PTS loading con-ditions. The necessary models for performing a probabilistic fracture-mechanics analysis for the Calvert Cliffs-1 reactor pressure vessel and the results of the analysis are discussed in the remainder of this chapter.

5.3 Calculational Models The conditional probability of vessel failure (through-wall cracking) was calculated for the Calvert Cliffs-1 reactor pressure vessel using the OCA-P code.3 0CA-P accepts as input the primary system pressure, the temperature of the coolant in the reactor-vessel downcomer, and the fluid-film heat trans-fer coefficient adjacent to the vessel wall, all as a function of time in a specified PTS transient. The code then performs one-dimensional thennal and

. stress analyses for the vessel wall and finally a probabilistic fracture-mechanics analysis. Details of OCA-P necessary for an understanding of the Calvert Cliffs-1 vessel analysis are discussed belcw.

1 i

b CC-5.6 5.3.1 Fracture-Mechanics Model The fracture-mechanics (FM) model in OCA-P-is based on linear elastic fracture mechanics (LEFM) and uses a specified maximum value of K Ia to account for upper-shelf behavior. The stress intensity factor (Ky ) is calculated using superposition techniques in conjunction with influence coefficients that were calculated using finite-element techniques. The application of this procedure makes it possible to perform a large number of deterministic FM calculations at reasonable cost, a necessary condition for performing the probabilistic analysis.

• The Calvert Cliffs-1 vessel was fabricated from sections of plate and has both axial and circumferential welds in the beltline region, as shown in Figs.

5.2 and 5.3. The length of flaws in the axial welds with depths greater than 40 mm was assumed to be approximately the height of a shell course, an'd the shape was assumed to be semielliptical (this flaw is referred to as the 2-m flaw). Since the ends of this flaw are fixed, propagation was judged on the basis of the K ratios (Ky/KIc' I IKla) at the deepest point of the flaw. Deep

axial flaws in tne plate region were assumed to be two-dimensional (infinite length) since their surface length could extend the full length of the core.

Shallower flaws were assumed to be two-dimensional, because long shallow flaws are essentially two-dimensional, and short flaws tend to grow on the surface to become long flaws,4 at least in the absence of cladding. Because the effect of cladding on the surface extension of stort flaws is not known at this time, any possible beneficial effect has been discounted.

Cladding on the inner surface of PWR pressure vessels was included in the OCA-P analysis as a discrete region to the extent that the thermal and stress effects were account for. As mentioned above, the effect of cladding on the surface extension of finite-length flaws was not considered.

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--CC-5.9 Because of the difference in the coefficient of thermal expansion between the cladding and base material, the calculated stresses in the cladding. exceed the' yield strength of the cladding by an appreciable amount, and this results in an overestimation of the K values g for the flaws, which were assumed to terminate in the cladding or extend through the cladding into the base material.

An alternative approach would be to limit the stress in the cladding to the because K is sensitive to the strain, yield stress, but this underestimates Ky g which is not limited by the yielding phenomenon. The difference in K gbetween these two extremes is not large; thus the conservative extreme was selected.

Paterial properties required for the fracture-mechanics analysis include the static crack initiation and arrest toughness values (K Ic and Kg ,) and the nil-ductility reference temperature (RTNDT). For the -probabilistic fracture-mechanics analysis, mean values of these parameters are required, and they i were obtained for the vessel material as follows:

K * '.43 {36.5 + 3.084 exp [0.036 (T - RTNDT + 56)]), MPa 5 (5.1)

Ic K = 1.25 {29.5 + 1.344 exp [0.0261 (T - RTNDT + 89)]), MPa m (5.2) la i

where the quantity in braces represca.ts the ASME Section XI 5 lower-bound tough-ness value and T is the temperature at the tip of the flaw in C. These ex-pressions were obtained by letting the ASME lower bound curves represent the mean' values minus two standard deviations (2a) and by letting c(gIc) 0.15 R Ic and o(g ,) = 0.10 K la*

In many cases, if crack arrest takes place, it must do so at upper-shelf temperatures, that is, at temperatures that, under static loading conditions, result-in ductile rather than brittle behavior of the material. Crack arrest under these conditions is not well understood but has been included in an

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CC-5.10 8 approximate manner by specifying a maximum value of K Ia that corresponds to the upper portion of an upper-shelf tearing-resistance curve. As illustrated in Fig. 5.4, which is a plot of K vs crack depth (a) and temperature (T) at a F 5.*

specific time in a transient, if ~ the load line (Ky vs a, T) intersects the If, Ia curve at Kla * (Kla) max, upper-shelf temperatures are not encountered.

K on the other hand, the load line misses the rising portion of the K Ia curve and then decreases, as it does for some transients, there is, according to the model, a possibility of crack arrest at upper-shelf temperatures.

The tearing resistance curve selected for this study represents a specific high copper, low-upper-shelf weld material that had been irradiated to a fluence of s1.2 x 10 19 neutrons /cm2 at a temperature of s300*C and tested at 200 C.6 The upper, nearly flat portion of this curve corresponds to a KJ value of s220 MPa 5, and this value was used for (Kla)maxiKJ was obtained using the relation Kg = ME (5.3) where J = strain energy release rate E = Young's modulus The tearing resistance of PWR vessel materials tends to decrease with in-creasing temperature and fluence, and thus the effects of temperature and fluence tend to compensate for each other through the wall of the vessel.

Because of this and the very approximate nature of the treatment of arrest on the upper shelf, no attempt was made to account more accurately for the effects of temperature and fluence on (Kla) max

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• The nil-ductility reference temperature (RTNDT) is equal to the sum of an initial (zero fluence) value (RTNDTg ) and an increase due to radiation damage (aRTNDT); that is, RTNDT = RTNDT g + aRTNDT (5.4)

The correlation for ARTNDT used in these studies was recently proposed by Randall and is ARTNDT = 0.56 [-10 + 470 Cu + 350 CU Ni] (F x 10-19)0.27 , C (5.5) or ARTNDT = 0.56 [283 (F x 10~19)0.194 - 48], C (5.6) whichever is smaller, where Cu, Ni = concentrations af copper and nickel, wt ".,

F = fast-neutron fluence (neutron energy > 1 MeV), neutror.s/cm 2

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Equctions (5.5) and (5.6) were derived.without' distinguishing between weld and base material. A more recent attempt to correlate.the data does dif-ferentiate between the two materials, and the results indicate (1)'substantially less damage for the base material than-for welds and (2) greater damage for the welds than indicated by Eq. (5.5).7 For this study, Eqs. (5.5) and (5.6) were used for the weld material, and a differential between weld and plate material was obtained from the most recent correlations7and was applied in the evaluation of flaw behavior in the base material.

The attenuation of the fluence through the wall of the vessel is approxi-mated with F=F ge -0.0094 a (5.7) where'F g is the fluence at the inner surface of the vessel and a is the i- crack depth in millimeters. The specific value of the coefficient in the exponent accounts to some extent for the effect of- space-wise spectral changes in radiation damage.7 If the assumption is made that a short and shallow surface flaw can extend on the surface through the cladding to become a long flaw (and this assumption is made for these studies), then it must be assumed that under the

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proper circumstances a very shallow flaw that initially resides entirely within the cladding can propagate radially. Unfortunately, the fracture-toughness properties of the cla'dding material are very uncertain, and the few experimental data that are available indicate a radiation-induced reduc-tion in fracture toughness similar to that for the base material. As an -

expediency, which may or may not be conservative, it was assumed that the cladding has the same fracture-toughness properties as the base material

[Eqs. (5.1), (5.2), (5.5) and (5.6)]. In the OCA-P analysis, assumptions regarc;ing the fracture behavior of the cladding influence only the initiation of very shallow flaws that initially terminate in the cladding. Under some circumstances, including the above assumption regarding the fracture toughness of the cladding, these shallow flaws will initiate and result in vessel failure.

Therefore,it was necessary to include the fracture properties of the cladding.

The deterministic fracture-mechanics model described above is used in OCA-P to predict the behavior of' a flaw during a specified PTS transient at a specified time in the life of the vessel, and the calculated behavior can be illustrated with a set of cri,tical-crack-depth curves similar to those shown in Fig. 5.5. The figure consists of a plot of crack depths corresponding to F5.5 various events and conditions as a function of the time in the transient at which the events or conditions take place or exist. Figure 5.5 includes (for 2-D, axially oriented flaws only) the locus of points for Ky=KIc (crac b initiation curve), Ky=KIa (crack-arrest curve), K y = (K y) max (warm prestress curve with i(y = 0), and Ky = constant (iso Kg curves). For times less than those indicated by the WPS curve, crack initiation will take place, but for greater times initiation will not take place unless perhaps there is a pertur-bation in K ythat negates the requisite conditions for WPS.

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The dashed lines in Fig. 5.5 indicate the behavior of two initially shallow flaws, ignoring the effects of WPS. The deeper flaw would initiate at a time of 42 min into the transient and would extend through the wall without arrest-ing. The other flaw would initiate at an earlier time, would arrest at a point 36% of the way through the wall, and then would reinitiate at a time of 48 min and penetrate the wall. Earlier in the life of the vessel the tendency for com-plete penetration of the wall is less.

5.3.2 Stress-Analysis Model When using the superposition technique in combination with influence co-

, efficients to calculate K ,g the stresses required are those at the crack plane in the absence of the crack and with no variation in the direction of the length of the crack. For the Calvert Cliffs-1 analysis, it was assumed that there was no azimuthal variation as well, and thus the one-dimensional stress analysis model incorporated in OCA-P was adequate.

Material properties required for the stress analysis included the coefficient of thermal expansion (a), Young's modulus (E), and Poisson's ratio (v). Although 0

these properties have some temperature dependence, it was determined that the use of appropriate average values results in an error in the calculated value of K yof less than 10%. Thus, average values were used based on the data in

, Ref. 9. The values used for the Calvert Cliffs-1 analysis are as follows:

Property Base Material Cladding 1

a. C 1.45 x 10 1.79 x 10 E, MPa 1.93 x 10 5 1.86 x 10 5 v 0.30 0.30 l

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. 5.3.3 Thermal Analysis Model Temperatures .in the wall of the vessel are required for two purposes:

to calculate the thermal stresses and to calculate the fracture toughness.

. The temperatures required for determining the fracture toughness are those in the plane of the flaw, while those used in the one-dimensional analysis of the thermal stresses must represent some type of average distribution through the wall. The thermal stresses in the vicinity of the crack plane are more sensi-tive to the radial temperature distribution at the crack plane than elsewhere.

Since these temperatures are the same as those needed for the fracture-toughness determinations, and since cnly one set of temperatures was to be used for both the stress and toughness calculations, the local temperatures would be the choice. These particular temperatures were not available, but fortunately the results of the thennal-hydraulic analysis indicated that for the transients of interest there was not much azimuthal variation in the downcomer coolant tem-perature. Thus, the time-dependent temperature distributions in the wal} of the vessel were calculated with the one-dimensional thermal-analysis model in OCA-P,using average downcomer coolant temperatures and heat transfer coefficients.

Material properties required for the thermal analysis include the thermal conductivity (k), specific heat (c p), and density (p) of the vessel material.

The values used are as follows:

Property Base Material Cladding k, W/m C 41.5 17.3 c , J/kg C 502 502 p

3 o, Kg/m 7830 7830

f CC-5.17' ,

M 5.3.4 Probabilistic Analysis Model The OCA-P probabilistic model, which is similar to that developed by Gamble and Strosnider 10 is based on Monte Carlo techniques; that is, a large number of vessels is generated, and each vessel is then subjected to a-fracture-mechanics analysis to determine whether the vessel will fail. Each vessel is defined by randomly selected values of several parameters that are judged to have significant uncertainties associated with them. The calculated probabil-ity of vessel failure is simply the number of vessels that fail divided by the total number of vessels generated. It constitutes a conditional probability of failure, P(FlE), because the assumption is 'made that the PTS transient (event) takes place. A logic diagram summarizing the various steps in the OCA-P probabilistic analysis is shown in Fig. 5.6. FS.6 The parameters simulated for the Calvert Cliffs-1 analysis are crack depth _

f(a), F ,g RTNDT, Cu, Ni, KIc, and Kla. Nofal distributions were assumed for all of these parameters except the crack depth; the standard deviations and truncation values used in the analysis are included in Table 5.1. T5.1 The probability of having a flaw in a specific weld with a depth in a specific range of crack depths dag is given by 1

P(aaj ) = NV f(a)B(a)da (5.8) ca j where N = flaws of all depths per unit volume of the specific weld V = volume of the specific weld f(a) = flaw-depth density function B(a) = probability of nondetection

I f, CC-5.18 s

k onNL.0WG 84 4t74 ETO

. n I DEFINE THANSIENT AND SIMULATE Kg ERROR l l CALCULATE T vs fatw, ti K

fr

' vs talw. tl ADVANCE TIME l l l l SELECT ME AN V ALUES CALCULATE K CP e f(RTNOT'lalal ggg g T lanw. ti.

COPPER K.,ERRORI RTNOT, I

NO r I O ISTHE CRE ATE A VESSEL SY K,1K ,21, TR A SIENT SIMULATING OVERP CRACK OEPTH ARTNOT ERROR  ; vgs YES WELO I ggg ADVANCE CR ACK OEPTH COPPER RTNOT, PLASTIC YES INST A81LITY 7 l CALCULATE RTNOT l NO l CALCULATE RTNOT l l

l SIMULATE K,, l SET CRACK CEPTH K,iK,* s l '

TO ARREST OEPTH YES NO NUV9ER OF CR ACK CEPT 645 NO E X M AUSTE O' YES

< AOD CNE TO NUYSEm , AOO ONE TO NUMBER 08sa: LURES OF NCNF AILURES I

ADO ONE TO NUM6ER _

CF TRIALS pea 80HMEO NO 'r[$fS5 YES CALOULA TE CON 31TIONAL PRC9A88LITY GF F AILUAE Fig. 5.6. OCA-P program logic.

-n ,- , -, , .-

, .,If CC-5.19 1

Table 5.1. Parameters simulated in OCA-P

~ Standard Parameter deviation Truncation (c)

Fluence (F) 0.3u(F) F=0 i Copper. 0.025% --

i flickel .0. 0 --

U

RTriDT, 9'C b ARTilDT 13'C b

K Ic 0.15p(K!c) 3a X

Ia 0.10 ,:(KIa) :3 1

"flormal distribution used. for each parameter.

3 -,

2 :1/2 C(RTiiDT) " C(RTilDT g ) + C(aRitiDT) ,

truncated at 30. -

i i

i ,

d 1

I CC-5.20 )I The parameters N and f(a) pertain to vessel conditions prior to preservice -

inspection.and repair, and B(a) is derived on the basis of repairing o'r other-wise disposing of all detected flaws.

The value of N and the functions f(a) and B(a) are not well known because most of the available inspection data do not pertain' to surface flaws that extend into and through the cladding of a PWR pressure vessel. For the Calvert Cliffs-1 analysis, the functions f(a) and B(a) were those suggested in the Marshall Report Il and are as follows:

t

.16 a (3,9) f(a) = 0.16 e

{

i B(a) = 0.005 + 0.995 e-0.113 a (5.10) where a = crack depth, m

( .

}f(a)da=1 o

For the Calvert Cliffs-1 vessel the probability of nondetection, B(a),

should probably be set equal to unity, independent of a, because it is not likely that a reliable inspection was made for flaws in and extending a short distance beyond the cladding. Furthermore, it is not likely that any detected flaws of this type were repaired. Even so, Eq. (5.1) was used in the Calvert Cliffs-1 analysis. If B(a) = 1 were used instead, P(FlE) would be about twice as much. Thus the results of this study can be interpreted accordingly.

The value of N used in the Calvert Cliffs-1 analysis was 1 flaw /m3 of weld and and t,ase material,/it was assumed that all flaws were inner-surface flaws normal to the surface. Flaws in welds were oriented in the length-direction of the weld, while those in the plate segments were oriented exially. The assumed value of the flaw density (1 flaw /m 3) agrees with that suggested in the Marshall Report,

CC-5.21 -

but the uncertainty is considered to be very large (values of N corresponding to lo variations are estimated to be 10-2 and 102 flaws /m), 3 The volume (V) of a weld ar plate segment used for calculating the number of surface flaws was the total volume of that portion of the weld or segment that was nearly within the axial confines corresponding to the active length of the core.

As mentioned above, the calculated probability of vessel failure for this-study is the number of simulated vessels calculated to fail divided by the total number of vessels simulated or otherwis9 accounted for. Thus, i

w P(FlE)=((y, V)N f(a)B(a)da , (5.11)

J VJ

, where 1

Njj=numberofvesselswithaflawinthejthregionthatfail N')

y = number of vessels simulated with a flaw in the jth region

, V3 = volume of jth region l The integral in Eq. (5.11) accounts for the vessels that have no flaws whatsoever, and each term in Eq. (5.11) represents the contribution to P(FlE) of each specified region of the vessel.

For very small values of P(FlE), the value of N'3 y required to achieve reasonable accuracy becomes quite large. Under some circumstances the value of N')

y can be reduced by using stratified sampling of one or more of the parameters simulated. This was done for the flaw depth, assuming a uniform distribution of depths. This procedure allows a more frequent sampling of i

the less probable deep flaws, which, for low-probability transients that are characterized by high pressure and a mild thermal shock, are responsible for most of the initiation events that lead to failure. The results are then

~

v..d-av; ..+

3 l< ' '

lCC-5.22 )I i

% v

.y 3 w

weighted by the actualIflaw-depth density tolbtain ,

~

x .

~

'[' 4 ((h)B(a)da aa W I

_ P(}lE) Ji = IIviJ N' d NV j [f(a)B(a)da, -

(5.12)

~"

m f(a)B(a)da

._ .. m where-Njjj = number of vessels that fail with'a flaw in the jth region with depth in aa g N'jj y = number of vessels simulated with a flaw in the jth region with depth in aa g A deterministic analysis is made for each of the simulated vessels to determine if failure will occur during a particular transient at a specified time in the life ~of the plant. Th'e criterion by which failure is judged is as follows: if, following an initiation event, K remains y greater than K Ia up to or beyond the point at.which plastic instability occurs in the remaining ligament, failure is assumed. The onset of plastic instability is evaluated on the basis of achieving an average pressure' stress in the remaining ligament equal to the flow stress. The flow stress is assumed to be independent of temperature and fluence and is specified as 550 MPa.

The number of vessels that must be simulated depends upon the accuracy requiredforthecalculatedvalueofP(FlE),andassmallanumberaspractical is used to minimize computer costs. The minimum number of simulated vessels required to satisfy a specified accuracy is estimated by applying the central w

h

,N 4

WI' CC-5.23 limit theorem.12 Using this approach and specifying a-95% confidence level  !

yields W

f(a)B(a)da (5.13)

P(FlE)3=P3 NV) 1.96 o3 o

where P(FlE)3 = true value of the conditional probability of vessel failure for those vessels having flaws in the jth! region only a3 = one standard deviation, P

Nf3 3=Ng*

For the direct approach (not using stratified sampling)

. . -1/2

• Pj (1 - P3 )

oj = NV (5.14)

Ny '3 3[f(a)B(a)da.

- . o a .

When stratified sampling is used, r 31/2 i f(a)B(a)da ,

aa P (1 - P )

oj = w n, ) NV 3[f(a)B(a)da, (5.15) i ff(a)B(a)da

- - U o

\ /

where P .

$3 =

The value of a corresponding to all of the vessels simulated is f "P(FlE)* "j , (5.16)

. . . , , , - , . _ - _ . _ _ _ _ , . - .m. ,-_ -__ y-. _, .- . -w ,. _ ,._.m_

1 7 5' l CC-5.24 l

and the . error, c), associated 'with the jth region is 1.96 o 3

(5.17) 6 HV f(a)B(a)da 3 3 The total error, c, considering all regions of interest is a,.

1.96'cP(FlE) c,= . (5.18)

P NV f(a)B(a)da 3 3 Three specific criteria were used in selecting the number of vessels to be simulated:

(1) (N;j) max = 00,000 (2) (N'3) y min = 10,000 (3) c3 = 10%

The application of these criteria in terms of ej vs P3 isshown in Fig. 5.7 F5. 7.

for the direct (nonstratified) sampling method.

For the purpose of estimating the absolute frequency of vessel failure or identifying dominant transients, the magnitude of the errors indicated in Fig. 5.7 was acceptable for most transients. However, for some transients and for the sensitivity studies, larger values of Nf3 and/or the stratified-sampling technique were used where appropriate to reduce the error.

5.4 Flaw-Related Data for the Calvert Cliffs-1 Reactor Pressure Vessel As already mentioned, the areas of the vessel of particular concern with regard to flaw propagation are the ones that are most likely to have flaws and

k

~

'}-

CC-5.25

'108-

~ ~

N'j.v . = 5 x 10' 10 " . 5 vN 'j 5 5'x 10'

• N'jv = 10" "

' 2

- 10 _ _

w W

g.

x i O E-C 10 -

4 i

, s ~

1 l

3

-m i, I 1 10"I  ! '  !

i 10-' 10-8 10 -

• 10-2 10-; 10-i 10-3 4

P.

J 4

~ 19. 5. 7. Gracnic illustration of the error in h

. ccnsistant with tr.e critaria used for es aoiishing the numcer of Oesseis simulated (l'.i.

vj-I i

1 i

CC-5.26 v relatively high values of F ,g RTNDTg , Cu and Ni. The region directly opposite the active portion of the core is exposed to the highest neutron fluxes, and the attenuation beyond the active length of the core is very steep. Thus, only this beltline region of the vessel was considered.

'Within the beltline region the concentration of copper is significantly less in the base material than in the welds, as indicated by the data in Table 5.2 and Figs. 5.2 and 5.3. However, preliminary OCA-P calculations (see Appendix K) indicated that because of their much larger surface area the plate segments would contribute significantly to vessel failure, assuming the same flaw density in both the plate segments and welds. These preliminary calcula-tions also. indicated that welds 2-203A,B,C and 3-203A, each of which is oriented in an axial direction, contributed far more than all the other welds. Thus, the regions of the vessel to be considered were these four axial welds and the plate segments. However, the contribution to P(FlE) of axial flaws in the plate segments was calculated for only a few of the transients and was not in-cludedinanyofthereportedvaluesofP(FlE)exceptasdiscussedinSect.

5.5.2 and Appendix K. This was done to maintain consistency between all tabu-lated values.

As discussed in Appendix K, the contribution of the one circumferential weld in the beltline region was relatively small because of the low concentra-tion of nickel and a much smaller value of Ky for deep circumferential flaws as compared to axial flaws of the same depth.

The information in Table 5.2 was taken from Refs. 13, 14 and 15; values "'

listed for chemistry, fluence and RTNDT were considered to be mean values.

l l

l l

CC-5.27 Table 5.2.

Material properties, fluences and volumes used in the LEFM analysis of the Calvert Cliffs-1 reactor vessel Material Chemistry Neutron fluence" " ter1al. b identification ,

at inner surface, I"fND vo .

Cu Ni 32 EFPY 3 18 2 ( C) (m )

Form Number (wt%) (wt %) (10 n/cm )

~

Plate D-7205-1 0.12 0.57 0.33 -12 0 D-7205-2 0.12 0.50 0.33 -12 0-D-7205-3 0.12 0.54 0.33 -12 0 D-7206-1 0.11 0.55 6.06 -7 2.43 D-7206-2 0.12 0.64 6.06 -34 2.43 D-7206-3 0.12 0.64 6.06 -12 2.43 D-7207-1 0.13 0.54 6.06 -12 2.08 D-7207-2 0.11 0.56 6.06 -12 2.08 D-7207-3 0.11 0.53 . 6.06 -7 2.08 Axial Weld 1-203A 0.21 0.85 0.33 -49 0

, 1-203B,C 0.21 0.85 0.17 -49 0 2-203A

• 0.21 0.87 6.06 -49 0.025 2-203B,C 0.21 0.87 3.03 -49 0.050 3-203A 0.20 0.71 6.06 -49 0.021 3-203B,C 0.20 0.71 3.03 -49 0.042 Cir Weld 8-203 0.35 0.74 0.33 -51 0 9-203 0.24 0.18 6.06 -62 0.139

" Maximum value in region.

b Volume within high-fluence region.

00-5.28 5.5 Results of Analysis 5.5.1 -Types of Analyses Conducted Probabilistic fracture-mechanics calculations were performed to determine (1) the conditional probability of vessel failure [P(FlE)] for a. number of postulated Calvert Cliffs-1 transients,-(2) the sensitivity of P(FlE) to small

changes in the mean values of certain parameters, (3) the.effect of including WPS, and (4) the effect on-P(FlE) of certain proposed remedial measures. The results of these efforts are presented below.

5.5.2 Conditional Probability of Vessel Failure The specific transients considered for a detailed OCA-P analysis are described in Chapter 3, and those actually calculated with values of P(FlE) 2 7 'are indicated in Table 5.3. For these transients the actual systems- 713 analysis output (primary-system pressure, reactor-vessel downcomer coolant temperature, and _ fluid-film heat-transfer coefficient) was used as input to ,

the OCA-P analysis, a'nd stratified sampling techniques were not used. Values ofP(FlE)forlessseveretransients[P(FlE)<10-7] were estimated in a con -

servative manner by using bounding transients and stratified sampling tech-niques. These transients were characterized by a step change in coolant tem-perature and a constant maximum pressure. None of the transients evaluated

• in this manner were dominant, and thus the possibly excessive degree of con-servatism was of no consequence. Those transients not calculated were judged

-7.

not to be dominant and to have values of P(FlE) at 32 EFPY less than 10

- For_all of the calculated transients with P(FlE) 210-7,valuesofP(FjE) were obtained for 32 and 41 EFPY. The latter time corresponds to RTNDTs (2c) =

132*C (270 F) for weld 2-203A, while 32 EFPY is the normal design end of life.

- Five of these transients were eventually tentatively defined as dominant, and t

y e *.r v* r* - * ~ ' -r-- *'v-** -*r ae v- = * * -

• v '---'-*~'rr- v ,e'-*e--+---**--v+

. s .r C0~5.29 Table 5.3. Summary of calculated values of P(FIE) for the Calvert Cliffs-1 postulated transients EFPY 9.2 16.8 24.4 32.0 41.2 53.0 19 2 1.52 3.03 4.55 6.06 7.88 10.24 F,,a 10 n/cm 46 66 79 89 99 110 RTNDT,,a C Trcnslent Conditional Probability of Failure, P(FlE) 1.3 6E-7 4.9E-6 1.4 3.3E-6 1.7E-5 1.5 3.0E-5 1.2E-4 1.6 5.1E-5 1.7 1.9E-4 4.8E-4 1.8 2.5E-4 6.2E-4 2.1 2E-7 1.4E-6 6.0E-6 2.4 2E-7 2.8E-6 1.7E-5 6.8E-5 2.4E-4 i 2.5 7.6E-6 3.2E-5 2.6 8.2E-6 3.4E-5 2.7 1.8E-4 4.5E-4 2

2.8 2.3E-6 1.1E-5 3.6 7.2E-6 3.6E-5 3.10 6.7E-5 4.6 2E-7 1.0E-6 4.13 6.0E-6 8.1 6E-8 4E-7 2.2E-6 8.8E-6 8.2 SE-7 1.2E-5 5.9E-5 1.5E-4 2.9E-4 5.9E-4 8.3 3.6E-4 1.9E-3 3.9E-3 5.9E-3 8.0E-3 1.0E-2 a Mean values at inner surface for weld 2-203A; add 33 C to obtain 20 value

[NRC 2cr screening value is 132 C (270oF)].

C0-5.30 for these, P(FlE) was calculated for additional values of EFPY. The corre-spondingplotsofP(FlE)vsEFPY,'F and

_ g RTNDTs are shown in Fig. 5.8. F5.8 Values of P(FlE) in Table 5.3 and Fig. 5.8 do not. include the contribu-tion of the plate segments. This contribution was calculated for transients No. 8.2 and 8.3 (dominant transients) and was found to be <5% for No. 8.2 and s50% for No. 8.3. Thus, for these two transients, factors of 1.05 and=1.5 can beappliedtothevaluesofP(FlE)inTable5.3andFig.5.8.

A summary of more detailed results for each of the four* dominant sequences at 41.2 EFPY (270 F RTNDT) is presented in Tables 5.4A, 5.48, 5.4C, and 5.40.

. Additional summaries are presented in Appendix L at 32 EFPY for each analyzed transient. These summary sheets provide data for a variety of histograms.

Four examples of histogram plots that can be produced from the summary sheets are provided for transient 8.3 in Figures 5.9-5.12.

Appendix L also includes for each transient calculated a definition of the transient input to OCA-P (downcomer coolant temperature vs time, primary-system pressure vs time, and fluid-film heat transfer coefficient at the vessel inner surface vs ti,me), temperature distributions in the wall, and a set of critical-crack-depth curves for weld 2-203A based on mean values of all parameters except Ic and Kla, which are -2e values, and 32 EFPY. Examples of these graphical K

outputs are shown in Figs. 5.13-5.16 for transient No. 8.3. -

5.5.3 Sensitivity Analysis ThesensitivityanalysiswasconductedbydeterminingthechangeinP(FlE) corresponding to a change in the mean value of each of several parameters. The mean value of only one parameter was changed at a time while all other parameters retained their original mean values. The parameters changed were Kge , Kla, RTNDT, Cu, F, fluid-film heat transfer coefficient, downcomer coolant temperature, primary-system pressure, and flaw density. The amount of the change for each parameter was one standard deviation, and the sign of the change was such that anincreaseinP(FlE) occurred.

The values of e used in the sensitivity analysis for KIc ' Ela, M DT, Cu, and F are listed in Table 5.1, and the values of the flaw density, N, corre-sponding to the application of la were 10 2and 10 -2 times the original mean j There are actually five dominant sequences identified in Chapter 6.0.

However since sequences 2.3 and 2.4 are assumed to be identical, data are provided in this chapter only for sequence 2.4.

m

.CC-5.31 E7PY 0 10 : 20 30 40 50 . 60 l I l I i i

/0 g[ , ,

f M. A

? :_ e

.* ./ .

• i

. / , a r__f. + .. . - ._ ; i _ - ._.r _ - _ - _ _ .

'j.

f- ,

• 4 ._. y .g __ L  ;- q n

i -/ -i:  ! i i-3a = --.... ,

• g -

't to ,

, / a <

/_

/

j. 8.L r

_ f_. . .____-. . . . . .

. . . . . . . . . . . . . _ . - . . . '3 f ,_ - . _ .__ -_:- _ - -

L 2, r- l

. e- +

r

_ / t

, l 4, < . >

10 .

_ . . . . . _ . _ . . . ... ~.

r g .. .. .- ... . . . .- . . . . . . . . . - . . . . _ _ . . . _ .

g ,

a I

/g _

-._s....._ g, I ._ _i _ .2 ._

/

__..._._..-..j..___.

...3

-g u-

'l._ _- .. .l. . -_ l a . .. . . .

f

. . - . _ . . . . . - ...^ . . . . _ . . . . .. . .. .. _ . . . . . ..

_i, ,.-

10 .- - .

.- . _ . _ _ . . u....... . . . . . .

. 4_..&.- _..

'l i  ?

l

_--: . . . . . - . . . . . . ,/ .. ,_.. . . _ _ . . . . _ _ _ ....

./

re .

i

,pe . F

, e

! 0* 2 4 6 8 10 12 Fluence (weld 2 203A),10" neutrons /cd

[ t i 1 .t F i 20 40 60 80 30 100 110 120 1 lIT2T- (weld 2 203A), 'C i 5 Fig. 5.8. P(FlE) vs EFPY for Calvert Cliffs-1 postulated PTS transients.

1 1

, , . , , , . -- - - - ., - - - - . - . . , . , - - .- - ., .g. . , . - ,g , - . , -

I I- T S C CLIFFS CLAU 2.1 1. FLAbS/M**J' FC = 7.c:6 C D 41 S

---

LhAdJUSTED-------------- ---ACJLSIEG---- .

t: E L C ... . .P.. (_F./ L. ) . . . . S S A.C A _ ..

.._2 E _lili...

F(1h111A) hev F(F/L3 .

2E66 . . . . _ h1 RIALS ..

I b.bzu-Ob 1.teC-C5 26.55 1.CSC-C2 C.02b 1.300-06 SCOOCC 2, C.CCu+0C C.CCL+00 0.0C 1 170-05 C.CSC 0.CCC+GC SCCCCC J 1 170-00 2 4CC-CL 154.CC 1.s50-04 C.C21 2.47C-CU bCCCCC' bdSSEL 1.4CD-Co 26.2C

+

OEP1HS F Cl; INIIIAL lb11lAllub (NF) 2.16 6.66 11 62 17.C3 22.S5 25.42 26.51 44.25 S2 72 huPLCh is (St 245 51 14 4 I C 0 P fliC L h 1 10 CS.C .

22.9 U.S 1.2 C.4 C.1 0.C 0.0 -

~

IIFES LF F A ILL64 C ( P I bL 10 5 )

0.0 AC.C 20.C 3C.C 40.C SC.C 6C.C 70.0 6 0. C' SC.C 100 0 110.C 120.C hLktLG C C 0 C 0 E 7 IJ B 11 1 0 PL6 CENT 0.C C.C 00 0.0 0.0 16.7 14 6 27 1 16.7 22.9 21 C.0 8e

.Ut Ihli1AIIGN I-84 (NC I ( C L C .C 3 U

-bS.c -41.1 -27.e -ia.s 0.c i2.5 27.e 41 7 $5.e es.4 82.2 s7.2 111 bbMdCG C 2 74 202 512 154 tS 22 0 0 C C*

PtHLEh! 0.C C.2 6.2 25.J 42.5 1c.2 7.4 18 0.0 .C.0 0.C 0.C AHHESI I-b it4J I t Ct.C 4 L )

. -27.6 -12.S 'O.C ~13.9 27.8 41.7 55 4 65 4 83.3 57.2 111 1 125.0 138.S huFtCH C 0 1 5 4 e 42 391 bt! 112 C 0 FEbtJh1 0.C C.0 C.1 C.d C.J C.7 2.1 24.1 SC.4 S.O O.C C.C Table 5.4( A). Summary sheet of OCA-P output for Calvert Cliffs-1 postulated transient flo. 2.1

.k*

e 1

l eJ I S 0 CLIFIS LLAC J .4 1. FLA%S/M*C3 FO- e 7 tEC0419 .

---

LhAOJLSTLU-------------- ---ACJUSILC----

DELC F ( F/13 ) SSAC1 AEbb P(INITIA) h*V F(F/E) 2El 6 b l I4 1 A L S I 2. 2 5 tJ- 0 2 1.itO-C4 / . *i l J . I '.2 0 - C J 0.025 5.c2C-CU 1600CC 2 4.11u-06 1 3tC-C5 JJ.12 7.iEU-CE C.CbC 4.CLC-Ou 60CUCC 3 9./JD-04 4.t2C-C5 S.7d 7.440-C4 0.C21 9.540-Cc 5C00CC .

VESSEL d.e2C-Cb 6.74 OLPTHS F C f. IN111AL lbl13A110h (EN) - **'-

~.

4.16 C.ct 11.62 17.02 24 95 25 42 Jc.51 94.25 52.72 -

hLNLEH 22 se2 a6e 12e 2e iC i i 0 PEbCENI 14 c2.2 23.c E.7 2.2 C.6 0.1 C.1 0.0 ,'<

I I Mii S LF FAILuhc(F1htIE5) 0.0 1C.C 20.C' 30.C 4C.C SC.C 6C.C 7C.C 80.C 'SC.0'100.C 11G.C 120.C huMLEH C C 0 32 121 54 15G 172 170 122 AC7 E2 PEbtENT 0.C ,C.C C.0 2.0 11.5 S.C 14.3 1c.4 16.2 11.6 10.2 7.6 o

?

Ih111AIILA I-hIhC1(CEC.0) u

- :2 5 . c -41.3 -27.2 -12.S 0.C 13.S 27.E 41.1 55.6 65.4 U3 3 57.2 111 1 u htFLE6 2 14 1Ca 50c ces all (22 420 13 0 0 0 PLHLLh1 C.1 C.5 J.9 19.0 25 1 11 7 23 2 10.C C.5 C.0 0.C C.0 A6HESI T -h 1840 I ( U E L .C. J

-4/.c -12.s 0.C 13.9 27.E 41.7 55.C 65 4 63 3 57.2 111 1 125.C IJb.S bu.vedh C C 0  !! 3 1 10 273 1155 155 C 0 FLECENT C.C C.C C.C 07 C.2 Co l 1.1 16.5 71.S S.6 0.C 0.0 l

Table 5.4(B). Sununary sheet of OCA-P output for Calvert Cliffs-1 postulated transient No. 2.4

" 8I* .g

). _

. ~ '

2 ,

_ ~ _

. ~ _

E' .

. ~

( .

~'

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Table 5.4(D). Summary sheet of OCA-P output for Calvert Cliffs-1 postulated transient No. 8.3 1

1 s

l Q l

l 6

i

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-d '

1CC-5.36

'OCR-P IPTS C CLIFTS CLAD 8.3 INITIRTION CRACK DEPTHS FO- 6.050E19 8

8-m 8- -

=

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[ig.5.9. Histogram of percent of initiations vs crack depth for first initiation event (Calvert Cliffs-1 postulated transient No. 8.3; 32 EFPY).

I

?

+ , - - e- -v e+e-y +.n- +--e yey~--.+,e - em ww tr~x-9-.r-r-t--ve-v*wwwe,---w-- r at--*--,tvye-m=?e---,---'-w ee-* e 'm r

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p CC-5.37 r OCR-P IPTS C CLIFFS CLSD 8.3 TIME OF FRILURE FC- 6.CSCE19 8

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0 10 00 33 40 50 63 70 80 90 100 1:0 120 III'.E, MIN.

Fig. 5.10. Histogram of percent of failures vs time of failure (Calvert Cliffs-1 postulated transient No. 8.3; 32 EFPY).

CC-5238 OCR-P IPTS C CLIFFS CLR0 8.3 o INITIRTICN T-RTNOT FO- 6.06,0E19 8

g_ _

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y 3. y o- y y y 4- g- p- 4- .,:.

T ~'!CT, OE3.C Fi g. 5.11. Histogram of percent of total initiations vs relative temperature at which initiations take place (Calvert Cliffs-1 postulated transient No. 8.3; 32 EFPY).

l i

., . _ .m .. . _._ _ . - . .

^

.~CO 5.39 c

l t

c OCR-P. IPTS C CLIFFS CLRD 8.3 e RRREST T-RTNOT FO 6.06CE19 i 8 L

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.s,,,,-. c.u t , t,:.e . v, Fig.'5.12. Histogram of percent of total arrest events vs relative temperature at which arrest events take place (Calvert Cliffs-1 postulated transient No. 8.3; 32 EFPY).

l.

i

- . , - . . . . . - _ ._ . _, . , _ . , , _ , . _ _ _ . , , . _ , . . _ . . _ . , . , . . _ , ~ _ , - . . . . . _ _ , . , _ _ . . , . _ , . _ . , _ _ _ , . , _ _ . _ .

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Fig. 5.13. P. T and h vs t for Calvert Cliffs-1 postulated transient No. 8.3.

l

t 4

3 l CC-5.41 tl' i i

IPTSCC:!TTSCL508.3 E . .

, Eo e n.m =

c R

- 88%.

r H.m a z.m Y 5:8 in:5 t ro.m h

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8, 03 0.4 c. c.s c.7 c.s o.s Fig. 5.14. Wall temperature vs a/w, t for Calvert Cliffs-1 postulated transient No. 8.3.

~

CC-5,42 4*

n IPTS C CLIFFS CLP.D 8.3 88:85

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Fig. 5.15. Wall temperature vs t, a/w for Calvert Cliffs-1 postulated transient No. 8.3.

q 7

-p

~

CC-5.43 CRITICRL CRRCK DEPTH CURVES FCR IPTS C CLIPPS CLR0 8.3 RTNOTC ~40.9 CEGC %CU - 0.21 %NI - 0.87 FO - 6.06E19 LONGIT x " 2-0 flaw o a "

x

) e x ,

+ e. 1r -

+

x Q +

/// K I =K

• g . x Ia o# . " -

+ .

+

m .

+

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O

. +

. , . w 2-m flaw 3 .. . x . o . . " -

x +

,,o,.... *7* ,.2-m flaw

• ........'.........< +

\ <

gd - x .

+ a o

• e < uj * , , . . . u = j x

+ a .  ! '

KI = 220 MPa di

- x + g , . o . .

x + * . .*** *****

, . n . -0 flaw d ~ >+ yS -

x xt o as

• Q I

=K Ic ( - -WPS

+ o#

d - 1 2' " -

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d -

x 0 " -

x $

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, , , f****?xxxTI99999999999999Ess=Pessnesessasi o to ao so to so so to ao so too tio 1:

TIMEfMINUTES)

Fig. 5.16. Critical-crack-depth curves for Calvert Cliffs-1 postulated transient No. 8.3; 32 EFPY, weld 2-203A.

1 1

g> ,

CC-5.44 )

value. For the sensitivity. analysis the change in the downcomer coolant tempera-ture considered was a linear change in temperature from zero' at time zero to 28 C (50 F) at a time corresponding to the minimum point in the temperature vs time curve. From then on, the change in temperature was a constant value of 28 C. The change in the heat transfer coefficient, h, was 0.25 h, and for the pressure it was 0.34 MPa (50 psi).

The results of the sensitivity study are presented in Table 5.5 for 41 T5.5 EFPY. Table 5.5 includes (1)thevaluesofP(FlE)atboth32and41EFPY corresponding to the original mean values of the parameters and (2) the ratio P(FlE),/P(FlE)41correspondingtoeachofthechanges.

It is of interest to note that aside from the sensitivity to N, P(FlE) is most sensitive to the reduction in downcomer coolant temperature and is least sensitive to variations in the arrest toughness, the heat transfer co-efficient and the primary system pressure. It is also of interest to note that the sensitivities are dependent on the transients.

5.5.4 Effect of Including WPS During many of the postulated PTS transients, the stress intensity factor Kg , for all crack depths first increases with time, reaches a maximum, and then decreases. For the shallow flaws that are generally responsible for the initial crack initiation event, once K begins g to decrease it does so through-out the remainder of the transient. This time-dependent behavior of K g may prevent failure of a vessel because a flaw cannot initiate while Kg is decreas-ing, even though Kg/K Ic 2 1. As mentioned earlier, this phenomenon is referred to as warm prestressing (WPS), and the time of incipient WPS is the time at which Kg becomes equal to zero.

C0-5.45 Table 5.5. Sensitivity of P(FlE) at 41 EFPY to la changes in the mean values of several of the simulated parameters a

P(FlE),/P(FIE)4; P(FIE) Simulated Parameter b At At F K ic K, g RTNDT Cu h T c P N Trcnsient 32 EFPY 41 EFPY +,cr -ar -ar + cr + ar + or 1.6 5.1E-5 1.8E-4 3.1 3.1 1.1 4.8 4.6 1.3 15.0 1.2 100 1.7 1.9E-4 4.8E-4 2.3 2.5 1.0 3.1 3.3 1.0 8.3 1.0 100 1.8 2.5E-4 6.2E-4 2.3 2.6 1.0 3.1 3.2 1.2 8.1 1.1 100 2.1 2E-7 1.4E-6 4.3 2.6 1.0 7.9 6.0 1.0 4.4 1.0 100 I 2.4 1.7E-5 6.8E-5 3.5 3.4 1.0 5.1 5.4 1.3 16.2 1.1 100 2.5 7.6E-6 3.2E-5 100 2.6 8.2E-6 3.4E-5 3.5 4.1 1.1 5.6 5.9 1.2 8.8 1.2 100 2.7 1.8E-4 4.5E-4 2.1 2.4 1.0 2.9 3.1 1.1 5.1 1.0 100 2.8 2.3E-6 1.1E-5 100 3.6 7.2E-6 3.6E-5 100 4.6 2E-7 1.0E-6 .

100 8.1 4E-7 2.2E-6 4.0 4.0 2.8 10.0 6.8 1.2 30.0 .3 100 8.2 1.5E-4 2.9E-4 2.0 3.8 1.4 3.1 2.7 1.1 11.0 1.3 100 8.3 5.9E-3 8.0E-3 1.3 1.8 1.0 1.5 1.5 1.0 2.3 1.0 100 aP(FIE)4 is value at 41 EFPY, which corresponds to RTNDTs + 2ar = 132 C (270 F) for usid 2-203A; h(FlE), is increased value of P(FIE) due to le change in each simulated parameter, one at a time.

b Parameter adjusted by le so as to achieve an increase in P(FIE) relative to P(FlE) et 41 EFPY.

00-5.46 For most of the Calvert Cliffs-1 postulated transients, WPS could be a factor because the calculations indicate that for these transients Kg does not

~become equal to X until after the time of incipient WPS. A typical case is Ic

illustrated in Fig. 5.5. \fhe reason for not including WPS in most of the cal-culations is that the Ky vs t curves for the shallow flaws are very flat, L

making it difficult to detennine where the maximum is. Furthermore, unfore-f 'seen perturbations in pressure and coolant temperature might exist and defeat WPS. Even so, it is of interest to see what the effect is for. the idealized transients, and the results of such a study are presented in Table 5.6.

For some transients, such as No. 8.3 (see Fig.5.dg.) there can be more For these transients, than one time during the transient at which Kg = 0.

l the time selected for incipient WPS was that corresponding to the maximum value of Kg .

Table 5.6 shows, for each of the transients considered, the time of incip- T5.6 ient WPS, the calculated values of P(FlE) without WPS included in the analysis, and the ratio of P(FlE) with and without WPS included. It is apparent that for these idealized transients the benefit of WPS can be large but is dependent on the transient.

5.5.5 Effect of Proposed Remedial Measures on p(FIE).

The proposed remedial measures considered in the fracture-mechanics studies were (1) reduction in the fluence rate. (2) annealing of the vessel, and (3) an increase in the initial temperature of the HPI coolant.

5.5.5.1 Reduction in fluence rate The reduction in fluence rate was assumed to take place on January 1,1985, and it was assumed to be the same at all critical locations in the vessel wall.

The effect was simply to change the proportionality constant between F, and

. EFPY beyond January 1, 1985. At this time the vessel will have been in service for s7 EFPY, and the fluence for weld 2-203A will be 1.1 x 1019 neutronshm2 .

I*

.r. -

CC-5.47 Table 5.6. Effect of including WPS in calculation of P(FlE) at 32 EFPY P(FlE) Time of WPS Translent w/o WPS (min) P(FlE),j,wpg 1.3 6E-7 18 <5E-2 1.4 3.3E-6 18 <1E-2 1.5 3.0E-5 18 <2E-3 1.6 5.1E-5 20 <2E-3 1.7 1.9E-4 18 <2E-3 1.8 2.5E-4 40 1E-!

2.1 2E-7 18 <1E-1 2.4 1.7E-5 50 1E-1 2.5 7.6E-6 15 <4E-3 2.6 8.2E-6 20 <4E-3 2.7 1.8E-4 50 2E-1 2.8 2.3E-6 18 <1E-2 3.6 7.2E-5 15 <4E-3 3.10 6.7E-5 4.6 2E-7 20 <1E-1 4.13 6.0E-6 8.1 4E-7 50 <E-1 8.2 1.5E-4 57 <2E-3 8.3 5.9E-3 100 5E-1 aP(FlE)

Included in Yegpg is the and analysis, value of P(FIE) with P(FlE),fewp3 is the WPS value without WPS Included l

L

4Y C0-5 48 The fluence rate beyond 7 EFPY for weld 2-203A was assumed to be constant andequaltoh.199x10 I9 /f, where f is a factor by which the fluence rate can be changed. Thus, ,

Fo x 10' 9 1.1 + 0.199f (t - 7) , (5.19) where

/ .

t = time of service, EFPY, The effectiveness of reducing the f .uence rate at 7 EFPY was evaluated at 10, 20, 32 and 50 EFPY for those, transients included in Fig. 5.8, using f = 2,4 and 8. The results for 32 EFPY are presented in Table 5.7, and for all 75.7 F S,C values of t in Figs. 5.17 and 5.18. f t.it 5.5.5.2 Annealing Annealing of the pressure vessel will increase the fracture toughness of the vessel material, and the amount of the increase will depend on the anneal-ing temperature and time, the chemistry of the material, and the number of times the vessel is annealed. Test results from small specimens indicate that essenti$11y full recovery of the initial fracture toughness might be achieved by annealing in the temperature range 400-450'C for s200 h.16 Although pre-liminary studies indicate that ,uch a process would probably be feasible in

/

CC-5e49 l

Table 5.7. Benefit of remedial measures, P(FlE)[s RM /P(FIE)w/oRM*

at 42 EFPY for dominant Transion Reduction in Fluence Rate on Jan.1,1985 P(FIE) Increase HPl Original Mean Rate Reduction Factor

• injection Value at Annealing Temperature Transient 32 EFPY 2 4 8 at 9 EFPY by 22'C 2.1 2E-7 h h h h 2.4 1.7E-5 5E-2 h h 2E-1 8.1 4E-7 h h h h 8.2 1.5E-4 2E-1 3E-2 5E-3 5E-1 1E-1 k 8.3 5.9E-3 5E-1 2E-1 8E-2 8E-1 4E-1

• P(FlE)wRM: P(FlE) with remedial measure.

P(F P(FlE)w/oRM b(FlE)wRM<10~7.lE)withoutremedialmeasure.

P e

~ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ . _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ . . _ _ _ _ _ _ _ _ _ _ . . _ . _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ . _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _

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,$p,=y Fig. 5.17. EffectonP(FlE)fortransientNo.8.2of reducing f.luence rate at 7 EFPY by factors of 2, 4 and 8.

CC-5.51

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5' CC-5.52 some PWR plants, the feasibility of annealing the Calvert Cliffs-1 reactor l vessel under these conditions has not been established. Nevertheless, for the purpose of this study it was assumed that the Calvert Cliffs-1 vessel would ba annealed when the plant achieved s9 EFPY. (Wanuary 1987), and that there would be complete recovery of fracture toughness. In effect, after annealing at 9 y, the fluence at 9 y would be zero. Thus, after 9 y, Fg x 10-19 (weld 2-203A) = 0.199 (t - 9) , (5.21) where t = total time of service, EFPY.

This fluence can be entered in Fig. 5.8 to obtain values of P(FlE) after annealing. The benefit at 32 EFPY of this assumed annealing situation is indicated in Table 5.7.

5.5.5.3 Increasino temperature of HPI coolant The effect of increasing the HPI coclant temperature was evaluated for transients No. 8.2 and 8.3. The injection temperature of the HPI coolant was 1 ~

increasedbye,ko~C,andthisresultedina17Chighertemperatureforthedown-v-

comer coolant by the end of the 2-h transients (the rate of increase was assumed to be linear with time in the transient). The benefit of this remedial measure at 32 EFPY is indicated in Table 5.7.

sian. E 3t

'CO-5.53 8

REFERENCES

1. F. J. Loss, R.' A.~ Gray, Jr. , and J. R. Hawthorne, Significance of Warm Prestress to Crack Initiation During Thermal Shock, Report NRL/NUREG-8165, Naval Research Laboratory NTIS, Sept. 29, 1977.

2. R. D. Cheverton and S.- K. Iskander, "Themal-Shock Investigations," in Heavy-Section Steel Technology Program Quarterly Progress Report October-December 1980, NUREG/CR-1941 (0RNL/NUREG/TM-437), pp. 37-54, Union Carbide Corporation-Nuclear Division, Oak Ridge National Laboratory.

3. R. D. Cheverton and D. G. Ball, OCA-P,-A Deterministic and Probabilistic Fracture-Mechanics Code for Application to Pressure Vessels, NUREG/CR-3618 (ORNL-5991), Union-Carbide Corporation-Nuclear Division, Oak Ridge National-Laboratory (May 1984).

'4. R. D. Cheverton D. G. Ball and S. E. Bolt, "Themal-Shock Investigations,"

in Heavy-Section Steel Technology Program Quarterly Progress Report April-June 1983, NUREG/CR-3334, Vol. 2 (ORNL/TM-8787/V2),.pp. 57-74, Union Carbide Corporation-Nuclear Division, Oak Ridge National Laboratory.

5. T. U. Marston (Ed.), Flaw Evaluation Procedures, ASME Section XI, Back-ground and Application of ASME Section XI, Appendix A, Special Report, EPRI NP-719-SR, American Society of Mechanical Engineers, Electric Power Research Institute, August 1~978.

6. Letter from F. J. Loss (NRL) to R. H. Bryan (ORNL), March 31, 1981.

7. P. N. Randall, U.S. Nuclear Regulatory Commission, personal communication to R. D. Cheverton, Oak Ridge National Laboratory.

8. R. D.- Cheverton and D. G. Ball, "Therntal-Shock Investigations," in Heavy-Section Steel Technology Program Quarterly Progress Report October-December 1982 NUREG/CR-2751, Vol. 4 (ORNL/TM-8369/V4), p. 68, Union Carbide Corporation-Nuclear Division, Oak Ridge National Laboratory.

9. ASME Boiler and Pressure Vessel Code, Section III, Division I, Subsection NA,

2. Appendix 1, American Societ'y of Mechanical Engineers, New York, 1974.

10. R. M. Gamble and J. Str.osnider, Jr., An Assessment of the Failure Rate for the Beltline Region of PWR Pressure Vessels During Normal Operation and Certain Transient Conditions, NUREG-0778, June 1981.

11. W. Marshall, An Assessment of the Integrity of PWR Pressure Vessels,,

United Kingdom Atomic Energy Authority, Second Report, March 1982.

12. R. Y. Rubinstein, Simulation and the Monte Carlo Method, Israel Institute of Technology, John Wiley & Sons, New York,1981, pp.115--117.

i 13. R. B. Pond, Jr. , letter to J. D. White, Re: Weld Data for PTS Studies -

Calvert Cliffs Unit No. 1, Oct. 27, 1983. '

t

)'

- . _ , . _ . _ . . _ - _ . _ _ -,~ , _._ _, ._. _ . , . . ,_ .

- SP-CC-5.54

14. M. E. Bowman, letter to J. D. White, Oct. 28, 1983.

'15. D..E. Peck, letter to S. E. Titland, Re: Materials Data.for A-49 Project, Oct. 21, 1983.

16. -J. R. ~ Hawthorne, Naval Research Laboratory, personal comunication to R. D. Cheverton, Oak Ridge National Laboratory.

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CC-K,1 APPENDIX X CONTRIBUTION TO P(FlE) 0F FLAWS IN THE CIRCUMFERENTIAL WELDS AND IN THE PLATE SEGMENTS Flaws anywhere in the beltline region of the reactor vessel will contri-bute to the probability of vessel failure. However, aside from the effect of flaw depth, some contribute more than others because of differences in orien-tation, length, local chemistry of the material, and local fluence. Axial flaws have the highest values of K g

, and in Calvert Cliffs-1 the axial welds have higher concentrations of nickel than the circumferential weld of concern and higher concentrations of both copper and nickel than the base material.

The difference in radiation damage between the axial welds and base mater-ial is rather large, and thus the extended surface length of an axial flaw in a weld tends to be limited to the height of a shell course, and for deep flaws this limit on surface. length results in significantly lower'K values y

than for much longer flaws. The extended surface length of axially oriented flaws in the plate segments is not limited to the height of a shell course, if the fracture-toughness properties in adjacent segments are similar. However, the extended length does tend to be limited to about the active height of the ccre by the steep attenuation of the neutron flux beyond the ends of the core. Flaws in circumferential welds may be limited in surface-length extension by azimuthal gradients in temperature, fluence and material properties, but .not by the length of the weld since it is continuous.

Thus far, the OCA-P fracture-mechanics model does not account for gradients in fluence and coolant temperature along the specified surface flaw path. In lieu of considering this sort _of detail, all flaws in the circumferential welds were assumed to be two dimensional. Axial flaws in the plate segments were also

q k.i CC-K.2 assumed'to be two dimensional for the additional reason that the maximum length- 1 to-depth ratio nearly corresponds to two-dimensional conditions.

The use of a two-dimensional model for flaws in the circumferential weld is probably quite conservative relative to the treatment of the other flaws.

However, as indicated below, even under these conditions the contribution o'f these flaws to P(FlE) is negligible, and thus the excessive conservatism is of no practical concern.

The contributions of flaws in the circumferential . welds and of axial flaws in plate segnents were calculated for the two most dominant transients (Nos. 8.2 and 8.3), and the time in the life of the vessel considered was 32 EFPY. The flaw density was assumed to be the same for all categories of flaws considered, and'since the total volume of the plate segments is much greater than that of the welds, the plate segments contributed many more flaws than the welds.

The chemistry, fluence, volume and initial value of RTNDT for each distinct region of the vessel consid"ered for the three categories of flaws (axial weld,,

axial plate and circumferential weld) are given in Table K-1 for the plate regions and in Table 5.2.,for the weld regions. In an attempt to account for the azimuthal variation in fluence in the plate regions, ea:h plate segment was divided into a one-third-volume region with high fluence and a two-thirds-volume region with lower fluence. Also, the initial values of RTNDT given in Table 5.2 for the plate segments were reduced by 33 C to account for a lower radiation damage rate in the plate segments than in the welds (see Sect. 5.3.1).

The results of the analysis indicate that for transient No. 8.3 the circum-

[ ferential flaws add s5% to P(FlE) and the plate segments s50%. For transient L No. 8.2, which is a less severe transient, the contributions were much less, being only 5% for the plate segments.

i

7 CC-K.3

' The dominant transients for Calvert Cliffs-1 (8.2 and 8.3) not only have-

'the highest frequencies of failure associated with them, but they also have the -

~highestvaluesofP(FjE). Thus, because of the trends observed in the above study it is expected that the contributions of circumferential-weld and plate-segment flaws to P(FlE) would be no greater for the other transients. Thus, the inclusion of these contributions does not result in different transients being dominant.

0 1

CC-K.'4 Table K-1. Material properties, fluences and volumes used inevaluationofplate-segmentcontributiontoP(FlE)

Cu- Ni F RTNDTo" V Region 2 3 (wt %) (wt%) (10"0/cm ) ( C) (m )

1 0.11 0.55 6.06 -40 0.81 2 0.12 0.64 6.06 -67 0.81 3 0.12 0.64 6.06 -45' O.81 4 0.13 0.54 6.06 -45 0.67 5 0.11 0.56 6.06 -45 0.67 6 0.11 0.53 6.06 -40 0.67 7 0.11 0.55 3.03 -40 1.62 8 0.12 0.64 3.03 -67 1.62 9 0.12 0.64 3.03 -45 1.62 10 0.13 0.54 3.03 -45 1.34 11 0.11 0.56 3.03 -45 1.34 12 0.11 0.53 3.03 -40 1.34 "These' values are 33 C lower than the actual values given in Table 5.2 to account for lower radiation-damage rate in base material relative to weld material.

d

1 CO-L.1 APPENDIX L COMPILATION OF RESULTS OF CALVERT CLIFFS-1 PROBABILISTIC FRACTURE-MECHANICS ANALYSIS Detailed results of the Calvert Cliffs-1 probabilistic fracture-mechanics analysis are-included in this appendix so that a more thorough understanding of the effect of the various assumptions used in the fracture-mechanics model and the different. inputs to the fracture-mechanics analysis can be obtained.

For instance, the duration of all postulated transients for this study was specified as two hours. In many cases most of the failures do not occur until late in the transient. If the duration of the transient were one instead of twohours,P(FlE)wouldbereduced.substantially.

Sets of data are included in this appendix for each of the transients for

--7 whichP(FlE)>10 . A set of data includes, in this order, (1) a figure of primary-system pressure, downtomer coolant temperature, and fluid-film heat-transfer coefficient vs time in the transient; (2) a summary of digital output that includes P(FlE) for each axial weld in the vessel, the estimated error in P(FlE),andhistogramdataforcrackdepths,timesandvaluesofT-RTNDTat the crack tip corresponding to initiation, arrest and failure events; (3) a plot of vessel wall temperature vs a/w, t; (4) a plot of vessel wall temperature.vs t, a/w; and (5) a set of critical-crack-depth curves obtained using -2c values of Ic and Kg ,, mean values of all other parameters, and fluences corresponding to X

32 EFPY. The various curves in the set of critical-crack-depth curves are identified in Fig. 5.16 (see Chapter 5).

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TIMES OF FAILURE (MI43TES) 0.0 10.0 20.0 30.0 40.0 50.0 50.0 73.0 90.0 90.0 100.0 110.0 120.0 NUMBER 0 0 0 0 0 9 20 56 66 50 47 35 PER0ENT 0.0 0.0 0.0 0.0 0.0 2.9 7.1 19.9 23 4 17.7 16.7 12.4 INITIATION T-RTNDT(DEO.C)

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' N'JMBER 1- 659 229 105- 33 13 4 1 0 ,

PERCENT 1.3. 62.6 21.8 10.0 ?.9 1.? 0.4 0.1 0.0 l l

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INITIATION T-RT1DT(DEG.C) /

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