Trends in the evaluation of the structural integrity of RPVs

Nuclear Engineering and Design 116 (1989) 73-100 North-Holland, Amsterdam

TRENDS

IN THE EVALUATION

73

OF THE STRUCTURAL

INTEGRITY

OF RPVs

E. V I T A L E

Associate Professor of Machine Design, University of Pisa, Italy Received 19 February 1988

The aim of this paper is to review recent trends, improvements and validations of methodologies for the assessment of reactor pressure vessel (RPV) integrity against the risk of leak or catastrophic failure, mainly deriving from the possible presence of crack-like defects at critical locations in the vessel wall. The first part of the work gives an overview of the input parameters, namely loading conditions, material properties and possible crack shape and dimensions, which are needed for a comprehensive fracture analysis of RPVs, discussing recent findings and still open questions about them. The next two sections are concerned with reviews of the presently available fracture approaches, related to both brittle and ductile fracture behaviour, and of probabilistic fracture mechanics methodologies. As conclusion, present limitations of methodologies for evaluation of RPV structural integrity and areas which need further improvements are outlined.

1. Introduction T h e severe consequences of failure of m o d e r n pressure vessels, coupled with the economic i m p o r t a n c e of reducing design conservatism, are leading to increased interest in techniques a n d methodologies for assessing reliability of these components. F o r nuclear reactor pressure vessels (RPVs), which are the only n o n - r e d u n d a n t c o m p o n e n t of the primary pressure-retaining system, b o t h the safety a n d the economical aspects are at an extreme a n d achieving cost-effective structural integrity is of primary importance. Consequences of R P V failure may be extremely severe owing b o t h to prevention of core flooding and to direct d a m a g e of core a n d other internal a n d external c o m p o n e n t s p r o d u c e d by the high energy release which can be associated with vessel catastrophic failure. It would therefore be possible, for a single event, to produce a large, uncontrolled release of fission p r o d u c t s by the sudden overcoming of barriers which are intended to limit the severity of o t h e r accidental sequences. Avoiding unnecessary conservatism may lead to significant reduction of m a n u f a c t u r i n g cost and, more important, m a y result in c o n t i n u e d acceptability of m a n y operating RPVs. Since the presence of crack-life defects, either from the m a n u f a c t u r i n g processes or i n t r o d u c e d during service, can never be excluded with current m a n u f a c t u r 0029-5493/89/$03.50

ing and inspection techniques, the R P V failure has mainly to be studied on the basis of Fracture Mechanics ( F M ) analyses, even if other failure modes (as e.g. plastic collapse) have also to be taken into account in some specific conditions. In this context the most severe outrage to vessel integrity comes from the c o m b i n a t i o n of thermal stresses, originated by rapid cooling transients, with high pressure stresses a n d degraded material fracture resistance resulting from c u m u l a t e d irradiation damage. Such a scenario is of p r i m a r y concern in Pressure W a t e r Reactor ( P W R ) vessels. Boiling W a t e r Reactor (BWR) vessels operate with a large inventory of water at saturation conditions so that any cooling transient would result in steam c o n d e n s a t i o n a n d system depressurization, preventing the coupling of high thermal a n d pressure stresses. In addition, B W R vessels have typical n e u t r o n fluxes m u c h lower than those experienced in PWRs, so that the end-of-life (EOL) fluence can be up an order of m a g n i t u d e lower a n d the p r o b l e m of r a d i a t i o n - i n d u c e d e m b r i t t l e m e n t is greatly reduced. For these reasons most of the work that will be reviewed in the forthcoming is mainly c o n c e r n e d with P W R vessels integrity. Nevertheless general criteria a n d methodologies are in principle applicable for every kind of RPV. In recent years, t h a n k s to the efforts a n d financial support of m a n y organizations, a m o n g which nuclear

© E l s e v i e r S c i e n c e P u b l i s h e r s B.V.

74

E. Vitale / Structural integri(v of RPVs

regulatory boards have played a leading role, the understanding of fracture mechanisms and of material behaviour in nuclear power plant (NPP) service conditions has been substantially increased. These acquisitions, combined with the increased potential of numerical calculations, have led to the possibility of applying complex and accurate methodologies, virtually accounting for all of the basic physical phenomena which can affect structural integrity. On the other hand, RPV failure modes may depend on many independent variables, and these may be so scattered, that different assumptions in design applications can result in deep differences of final reliability. In this context, it has to be recognized that the classical deterministic approach, based on the binary concept of "safe" and " u n s a f e " and which gives no quantitative estimation of actual safety margins (which result from random combination of independent variables), may be often inadequate and that a probabilistic methodology has to be applied in order to achieve a comprehensive assessment of safety against RPV failures. The purpose of this paper is to review recent trends, improvements and validations of methodologies for the assessment of RPVs structural integrity, outlining the basic features of both deterministic and probabilistic approaches.

2. Background

The comprehensive assessment of RPV structural integrity requires the evaluation of a very large number of factors by means of a complex interdisciplinary approach, including plant operation and event-tree analysis, thermal-hydraulics and stress analyses, material properties evaluation and Fracture Mechanics applications. Independent of the failure assessment methodology chosen, the fundamental inputs that must be provided are: - loading conditions, material properties, - possible crack shape and dimensions. For several aspects in these three areas a consolidated design philosophy has not yet been achieved and they are being actively investigated. Critical points that have been addressed in recent activities are reviewed in the forthcoming sub-sections. 2.1. Loading conditions

Loading conditions that have been recognized to affect the RPV integrity are essentially (besides normal

pressure stresses): cold overpressure test, temperature and pressure transients, - residual stresses. The relevance of these loadings for RPV structural integrity is briefly discussed below. Cold overpressure test

Pressure tests are usually performed on RPVs both at the end of the fabrication process and just after installation ( " s h o p " and "field" hydrotests, respectively). They are called " c o l d " overpressure tests since the test temperature is well below the operating temperature of the vessel (but normally higher than room temperature) and pressure is required to be not less than 1.25 times the design pressure. It could be argued that these test conditions may help estimating what flaws are existing in a vessel, since flaws over a certain length would produce failures. In other words, since load and temperature conditions are more severe than those in operation service, it could be concluded that a successful overpressure test gives an assurance of RPV integrity, at least at the time of the test. Unfortunately, calculations [1,2] of the limiting defect sizes for vessel failure (minimum size of defects that will cause failure) indicate that cracks from about 40 to about 160 ram, depending on material toughness and test temperature, can survive the initial pressure test. These defect sizes are smaller than for any normal, upset or test condition but, if the present reliability of non destructive examination ( N D E ) techniques is considered, they are very unlikely to have escaped preservice inspection, so that little or no improvement of reliability is obtained. Improved resolution for defect sizes could be obtained from pressure tests at lower temperatures. It is however generally agreed that the advantage of reducing the limiting defect size does not justify the increased risk associated with tests. The same conclusion is derived from considering the possibility of applying increased overpressures, especially if the risk coming from additional possible failure modes (e.g. stable and unstable tearing) is considered. At the light of these analyses the actual role of cold overpressure tests has to be found in the contribution in reducing residual stresses and in detecting (by failure) the very unlikely presence of regions where welding procedures, post-weld heat treatment (PWHT) or N D E were of lower than specified standards, resulting either in extremely reduced material properties o r / a n d non detection of unacceptable cracks.

E. Vitale / Structural integrity of RP Vs

75

sients may be divided, for a given difference between initial and final wall temperature, in two kinds: - transients which cause appreciable stresses within a small fraction of the vessel wall; - transients which cause a stress gradient all over the wall thickness. The second kind of transient (generally relativelylong, accidental transients) subjects the vessel wall to a m u c h larger b e n d i n g m o m e n t , a n d causes the higher risk of deep crack p r o p a g a t i o n t h r o u g h the vessel wall. T h e possibility for a thermal transient to generate these conditions depends on a n u m b e r of factors such as: final wall temperature, effective heat transfer coefficient, - duration, - conditions of the p r i m a r y coolant flux. A l t h o u g h it is out of the scope of this p a p e r to

Temperature and pressure transients T h e r m a l transients, which cause more or less rapid variations in system pressure and coolant temperature, can b e divided in two main groups: normal, upset a n d test transients, emergency a n d faulted transients. T h e former group corresponds to frequent transients, which produce relatively low stresses at a n y location; these stresses may however produce fatigue crack initiation a n d growth, possibly e n h a n c e d by corrosion mechanisms. T h e latter group is expected to produce the highest stresses in the vessel, a n d generally gives limiting conditions to materials properties requirements, even if acceptable safety factors are usually lower than those required for the previous group. F r o m a stress analysis point of view thermal tran-

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76

E. Vitale / Structural inte,grit3' of RP Vs

discuss the complex topic of transient evaluation it seems of interest to give a brief outline of some thermal-hydraulics problems of f u n d a m e n t a l importance for structural analysis. Particularly, estimations of thermal mixing p h e n o m e n a and heat transfer coefficient ( H T C ) have a direct and strong influence on the calculated structural response. If a transient results in high pressure injection (HPI) systems actuation, the degree of mixing of cold water (typically 2 0 ° C ) with the hot loop flow in the cold legs a n d the d o w n c o m e r annulus (see fig. 1) determines the m i n i m u m fluid t e m p e r a t u r e to which some portions of the vessel wall may be exposed. In general the worst condition is reached in those events which produce loop flow stagnation during HPI. Loss of continuous loop flow can in fact result in some degree of thermal stratification along the cold legs a n d in this case a strip of vessel material u n d e r the cold leg p e n e t r a t i o n might be exposed to a very cold water stream. This condition must be carefully considered when defining the limiting transients for vessel acceptability analysis. At present b o t h simple, a p p r o x i m a t e models a n d complex three dimensional codes [3 7] are available to perform mixing analyses on the basis of traditional thermal hydraulics results. The actual HTC, as function of time during the transient, is a very difficult p a r a m e t e r to predict, since its evaluation requires consideration of a n u m b e r of complex three-dimensional p h e n o m e n a [8,9]. However the importance of the H T C on the evaluation of vessel effective stresses is at some extent limited by heat c o n d u c t i o n mechanisms in the vessel wall [9]. A n H T C of 10000 W / m 2 ° C is an upper limiting value [10] b e y o n d which the t e m p e r a t u r e distribution, and hence the stresses in the wall thickness, will not be influenced. Of course, d e m o n s t r a t i o n of lower H T C values, when possible via a detailed analysis, will greatly help in reducing calculated stress and consequent failure risk. M a i n t a i n m e n t of system pressure or repressurization during the thermal transient will lead to the m a x i m u m danger of vessel failure, owing to the c o m b i n a t i o n of higher stresses and reduced temperature. These transients are generally referred to as Pressurized Thermal Shock (PTS) transients, and, at least in the last decade, have been considered as the m a x i m u m challenge for P W R vessels integrity. Prediction of event scenarios that may lead to RPV PTS has to be based on event-tree analyses and operating experience (e.g. Licensee Event Reports LERs); studies in this field can be found in [11-13] a n d will not be discussed herein. Briefly, we shall outline that at least the following events have to be considered as

potential PTS initiators: small-break loss of coolant accidents (SBLOCAs), main steam line breaks (steam line ruptures, stuckopen relief valve, etc.) - steam generator overfeeds. Studies that have been p e r f o r m e d to date indicate that events which may lead to severe PTS scenarios (such as those listed above) have a n estimated frequency in the range of 10 2 to 10 4 per reactor year for generic U.S. plants. The operating experience a n d the analysis of several PTS events occurred in the U.S.A. (e.g. the Three Mile Island 2, which resulted in severe core damage) have shown that the first protection against PTS is to ensure that the plant operating staff have the training, equipment and procedures necessary to preclude or mitigate a b n o r m a l overcooling events [14,15]. In this context the role of structural analysis shall be that of providing (as will be shown in sections 3 a n d 4) pressure-temperature limit curves to be used in emergency operating procedures and for operators training. Residual stresses

Residual stresses are generally present in RPVs as consequence of heavy section weldments, austenitic strip cladding and repair welding. The a m p l i t u d e of these stresses, d e p e n d i n g on welding parameters and PWHTs, is very difficult to predict or measure and extensive work is still needed before they can be accurately characterized. In addition, models to take into account residual stresses in fracture mechanics analyses still need i m p r o v e m e n t s a n d extensive experimental validation. It is therefore clear that extreme care a n d conservative a s s u m p t i o n s have to be used in h a n d l i n g these stresses for structural integrity assessment. Thick section welding causes residual stresses whose peak values are of the order of yielding resistance. P W H T s can sensibly reduce these levels hut it is commonly agreed that i m p o r t a n t stresses t a g remain at some critical location. Stress levels of 50 M P a are c o m m o n l y employed in fracture analyses [1] and, since direction a n d location of actual stresses are heavily uncertain, they are often a d m i t t e d to act b o t h parallel a n d transverse to weldments (equi-biaxial stresses), uniformly through the wall thickness. The large heat inputs associated with austenitic material cladding cause large biaxial stresses b o t h in the clad itself and in the underlying ferritic material. Even after the P W H T and the stress relief produced by the cold overpressure test, values of the order of the tensile yield, typically 300-350 MPa, are likely to remain in the clad. If o r is the operating stress in the ferritic material

E. Vitale / Structural integrity of RP Vs

at the cladding interface, it can be conservatively assumed that a stress of 3 5 0 - o r MPa is present in the austenitic clad in the same direction. This stress will also be temperature-dependent, due to the different thermal expansion coefficients of the austenitic and ferritic steels. A state of-the-art review of treatment of residual stresses in relation to the integrity of RPVs can be found in [16].

2.2. Material properties

As a consequence of continued evolution of materials and fracture mechanics analyses the need for accurate measurements of material properties is growing more and more stringent. Material properties which are relevant (besides the conventional mechanical quantities that are usually employed in structural analysis) to the fracture assessment of RPVs can broadly be divided in three categories: (a) properties which characterize brittle behaviour; (b) properties which describe mechanisms of ductile fracture; (c) fatigue crack growth properties. For each category both "as received" condition and the service-induced damage (which derives from the combined effects of neutron irradiation, thermal ageing and strain ageing) should be extensively characterized in order to allow evaluations of structural reliability at the beginning of service and at EOL. Characterization of the possible brittle behaviour of irradiated materials is of primary concern for those RPVs which were built before the middle seventies, when the effect of chemistry on irradiation-induced damage was not well characterized and copper and nickel contents in weldments were not carefully controlled, thus resulting in possible strong embrittlement at or before EOL. With the availability of improved materials and welding techniques the m o d e m philosophy of design is that RPV materials should be kept in the region of ductile behaviour during all potential pressure and temperature transients. The second category of properties is then of interest mainly for modern vessels and new designs. As outlined in section 2.1 fatigue crack growth properties are used to assess the damage introduced by repeated stress cycles induced by normal and upset transients, i.e. to infer possible crack sizes at any time during the RPV operating life, starting from postulated initial defects. This kind of analysis is of concern for

77

both old and m o d e m vessel and must include the possible effect of environmental interaction. Finally, we could put in a separate category fracture properties related to the austenitic cladding layer. The effect of cladding on the structural integrity of RPV has long been neglected, assuming that it would have very poor or slightly beneficial effects. However, it has recently been proposed that the presence of a tough surface layer can to some extent prevent a short surface crack from becoming a more dangerous long crack and this has promoted research activities focused to evaluate the fracture resistance of weld-deposited clad materials. Referring principally to U.S. plant designs, plate materials generally used in the fabrication of early pressure vessels were A S T M type A212-B or A302-B or their modifications, while more recent plate-type vessels are fabricated from A S T M A533-B Class 1. Early forgings were made of A S T M A105 or A S T M A336, while at present A508 Class 2 a n d / o r 3 are employed [17]. In the following, if not differently specified, reference will always be made to A533-B and A508 steels. Brittle behaviour As will be illustrated in section 3.1, the evaluation of the possibility of brittle RPV failures is based on the knowledge of the material fracture toughness parameters which indicate resistance to either crack initiation (Kit), crack arrest (Kia) or dynamic cracking (Kid). These quantities are evaluated by tests (for example, the standard A S T M E399 Kic test [18]) conducted at several temperatures on laboratory specimens usually taken from the material in the basic reference condition. Evaluation of high Kic values in the upper transition region requires the use of very thick specimens (up to 25 cm and more), which is obviously very expensive and almost not feasible for irradiated materials. Approximate values can however be obtained from specimens smaller than those required for valid standard tests, by application of empirical relationships or corrective techniques [19-23]. In order to characterize different material conditions the current practice is to assume that toughness values are independent of material condition if plotted versus the test temperature minus the Reference Temperature of Nil Ductility Transition (RTNDT). The RTND T is derived by Charpy-V tests, essentially be determining a temperature T~ above which energy is equal to or greater than 68 Joules and lateral expansion equals or exceeds 0.89 mm; RTND T is then taken equal to T~ - 33°C. This procedure relies on the assumptions (based on a relatively sound experimental evidence [20-23,30]) that the shape of the toughness vs temperature curve and the

78

E. Vitale / Structural integrity of RPVs

effect of irradiation d a m a g e are practically i n d e p e n d e n t of the material initial RTNDT, and that t e m p e r a t u r e shifts measured by C h a r p y - V tests are well correlated (typically within + 1 5 ° C ) with shifts of actual toughness data. Materials from different heats and having received different heat treatments, as well as irradiated materials, can therefore be acceptably characterized by a relatively low-cost set of C h a r p y - V tests. Reference curves c o n t a i n e d in Appendices to Sections III a n d XI of the A S M E Boiler and Pressure Vessel Code [24], which are based on data from several heats of A533-B and A508 base and weld materials, are i n t e n d e d to be used by this kind of correlation (i.e. via RTND T values). The A p p e n d i x G of A S M E III, to be used at a design stage in order to assess the significance of postulated flaws, uses a " K i n " reference curve which is i n t e n d e d to be the lower b o u n d of K k, K]a a n d K m toughness data, as it is shown inf fig. 2 (KI~ data are in general not relevant, since they are m u c h higher than Kl~ a n d K m values). The A p p e n d i x A of A S M E XI, which is concerned with the acceptability analysis of actually detected defects, a d o p t s K ~ a n d Kj~ reference curves; the first (Kl~) curve is derived as a reasonable (but not absolute) lower b o u n d to experimental data (see fig. 3), while the K ~ curve is substantially coincident with the A S M E I l l KIR curve. U p p e r truncation toughness values are set at 187 M P a m ~/2 for the K~R curve and 220 M P a m ]/2 for the K i t and Kla curves. While the use of these characterizing procudures is at present consolidated, some basic questions still remain concerning the significance of these toughness data with respect to integrity evaluation in actual c o m p o n e n t s a n d

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79

E. Vitale / Structural integrity of RPVs

past. On the other hand, for the upper part of the transition curve, specimen thicknesses required for valid A S T M Kic measurements may be greater than the thickness of plates and forgings used in the fabrication of RPVs, so that the use of valid K~c data in this region, besides requiring difficult and expensive testing, would be unnecessarily conservative. A possible solution to avoid this overconservatism could be the use of thickness-dependent toughness data derived from tests on the maximum thickness of interest [29,30]. In regard to arrest properties (Kia) the implications of crack front length are even greater than for initiation. In fact, while initiation is likely to occur from short surface cracks, arresting flaws are likely to have grown significantly in length as to become very long cracks. The other key-problem for arrest characterization is to provide and evaluate data in the transition region of the toughness curve. On one hand, some recent data on weld material fall below the A S M E lower bound KI, curve (see fig. 4), indicating that there is a possibility that the sharp upturn of the reference K I . curve significantly overstates actual Kia values in the region around T - R T N D T = 100°F. On the other hand results from the U.S. Heavy Section Steel Technology (HSST) program [31,32] and Japanese ESSO tests [33] indicate that crack arrest may be expected at toughness values up to 350 MPa rn1/2 (see fig. 5) so that the upper limit of 220 MPa n~/2 in the A S M E Code is probably unnecessarily conservative. These apparent contradictions may indeed depend on the large scatter that is typical of arrest toughness data, coupled with the fact that very few data are at present available in the region of T - RT~D T >

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1 2 0 - 1 5 0 ° F ( 4 9 - 6 6 ° C ) . However, there are some preliminary indications that the material upper shelf energy level may be directly correlated to the upper transitional arrest behaviour. Another fundamental parameter that strongly affects the risk of RPVs catastrophic failure is the irradiationinduced embrittlement. The early characterizations of irradiation-induced damage (e.g. Reg. Guide 1.99, Rev. 1 [34]) were mainly based on results from specimens irraidated in test reactors at enhanced fluxes and in neutron spectra having average energies larger than those typical for PWRs. This was done in order to obtain EOL (typically 32 Effective Full Power Y e a r s - E F P Y ) reactor fluences in a few years (for evaluation of neutron fluence normally reference was made to the portion of the energy ( E ) spectrum with E > 1 MeV). It was already evident from these data that details of the material chemical composition (particularly copper and nickel contents) and the irradiation temperature could greatly influence the increase in RTND T at a given value of the neutron fluence. As test data from surveillance specimens of actual licensed reactors have begun being available, the influence of spectral distribution and flux has been increasingly understood. Surveillance specimen data generally indicate a larger shift of the RTND T at low fluences as compared to accelerated tests, but the rate of increase in the shift becomes slower as the fluence increases [14]. The lesser fluence exponent is thought to be related to the lower damage rate in surveillance specimens, which provides more opportunity for the

80

E. Vitale / Structural integri(v q[ RP Kr

temperature-induced annealing of damage to occur during the period of irradiation. Surveillance data have also provided a better characterization of irradiation damage inside the vessel wall, where both the spectrum and the flux are degraded relative to the inner surface. Particularly, the spectrum is shifted toward a lower average energy, with many neutrons below 1 MeV contributing to damage. To account for this increased damage it has been recommended [14] that Displacements Per Atoms (DPA) must be used, instead of fluence greater than 1 MeV, as a measure of irradiation exposure. This would lead to predict greater estimated temperature shifts deep in the wall of the reactor vessel and hence a more uniform distribution of damage. There are indeed indications [35] that in vessels with high copper content (>__0.15 wt%) embrittlement will be almost uniform across the vessel wall, over a period from about 50% to 100% of service life. Another important result of recent work in this field is the more direct recognition of the high variability that affects measured final RTND T values of irradiated materials, as a consequence of combination of the variability of several factors such as: (a) the neutron spectra, flux and fluence; (b) the irradiation temperature; (c) the initial RTND T value; (d) different chemical compositions at different locations (for example, for weld materials a variable copper content may result from a variable coating thickness of the weld electrodes). Sensitivity analyses [14] show that the typical uncertainty of a few hundredths of a percent of copper or a few tenths of a percent of nickel results in an uncertainty of 2 to 5 E F P Y needed to achieve a given RTNDT; a 1 0 ° F uncertainty in assumed initial RTNDT results in a 1 to 2 E F P Y uncertainty; a fluence uncertainty of _4-40% gives a RTNDT uncertainty of about 25°F. Studies of this kind have led to the proposal of more directly accounting for statistical variations in the conservative evaluation of final reference temperatures. As representative of the current practice in irradiation damage evaluation the proposed Rev. 2 of the Regulatory Guide 1.99 [36] may be taken as reference. Fig. 6 shows the comparison of EOL arrest toughnesses predicted in the vessel wall (supposed to be at uniform temperature) by Reg. Guide Rev. 1 [34] and the proposed Rev. 2 [36] (considering weld material); it can be seen that prediction of arrest of deeply propagating cracks could be overly optimistic if based on the older shift curves, particularly for high copper weldments. Concening materials employed in last years, in which copper content has been kept very low, recent experiments show that phosphorus content also plays an

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important role, so that even Rev. 2 equations must not be seen as a final and completely reliable method for evaluation of irradiation damage. Finally, it must be outlined that data up to date reviewed about irradiation damage are mainly in the form Charpy-V and Kxc tests. Another question that has to be investigated is the effectiveness of these data to reproduce the effect of neutron irradiation upon crack arrest properties. Research activities are currently being carried out in this field [37], but published data are still very incomplete. Other aspects of in-service degradation of material properties, not treated here for the sake of brevity, may be found in [29].

Ductile behaviour The analysis of RPV fracture behaviour when the material displays sufficient ductility as to be no longer in the field of L E F M requires the use of properties that are able to characterize the onset, growth and final instability of a ductile crack. Research in this field is being actively carried out in many countries and several parameters have been proposed for use in structural analysis. While it is out of the scope of this paper to review this wide subject, a brief outline will be given of methods most generally employed in the field of structural analysis of RPVs. Ductile shelf and upper transitional behaviour is widely being evaluated in terms of the Rice's J-integral [2,30,37-42], i.e. by measurement of J values during the onset and growth of a ductile crack ( J - A a or J-resistance curve), eventually up to the beginning of unstable

E, Vitale / Structural integrity of RP Vs 35¢

definition of ductile crack "initiation" (J~c), since it is widely agreed that current standard methods (as the ASTM E813 procedure [18]) are not yet completely satisfactory. At present, small (at least for ferritic materials of interest for RPVs) but systematic differences are found among both J~c values and J - R curves measured by different experimental methods (e.g. the ' unloading-compliance' and the 'potential-drop' techniques for crack extension measurements) [38], so that a careful and conservative use of these parameters should be recommended. In addition, limitations exist for stable crack growth to be completely controlled by J-integral values [43], and this has to be conservatively considered in the use of experimental curves. Nevertheless, reference data are being at present produced (mostly by the unloading-compliance technique) for both irradiated and unirradiated materials. Upper shelf data for typical plate, forging and weld RPV materials are shown in fig. 7, while the effects of temperature and irradiation on J - R curves are shown in figs. 8 and 9, respectively. Without discussing details of experimental data produced up to date, an evaluation of the present status can be summarized by the following statements: (a) the temperature variation of upper shelf toughness and J - R curves, i.e. a decrease of both toughness and J-resistance slope as the temperature is increased, must be taken into account;

X

30( --_

II 0

_ ~ ~ --I) 4S~38114501"

------

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l

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TEMPERATURE

METAL

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Fig. 7. Comparison of upper-shelf toughness data for typical plate, forging and weld RPV materials (from [30]).

tearing, and definition of a crack "initiation" toughness, Jlc- Particular effort is being devoted to the development of reliable, possibly single-specimen, techniques for J-resistance ( J - R ) curve measurement and accurate

I

5

'

i

*

81

I

i

60"C

o 150"C

. 220"C • 290°C

j .

,5~. ~.~°

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2

2.5

GROWTH mm

Fig. 8. Effect of temperature on J - R curves for an A508 Class 3 forging (from [2]).

82

E. Vitale / Structural integrity of RP Vs ]

0

t

--

r

T

T

j T trr(ld = 290°C, T~,~p : 290"C 25~m C S , 20% s g e : 1 , IOT~ n c m ~ ( [

~1

MeV)

~s~ O

/

~ t,L,

--L lr w t-J

c

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/

i

0

~

i

05 Crock

10 Growth

A

1.5 8Olx,mm

Unirrod

Irrod

F]

o

•

Ft.

o I

•

LO

2

Fig. 9. Irradiation effect on J - R curves for an A508 Class 3 forging (from [2]).

(b) the effects of irradiation d a m a g e on u p p e r shelf initiation toughness seem to be almost negligible [2] for fluences < 1019 n / c m 2 ; at higher fluences modern A533-B a n d A508 steels exhibit a noticeable decrease of u p p e r shelf toughness, but the a m o u n t of the decrease seems to be badly correlated to the n e u t r o n fluence values [42]; (c) irradiation effects on J - R curves consist of a slight decrease of the J-resistance slope at fluences between 1 × 1019 a n d 6 × 1019 n / c m 2 [2,42]; (d) derivation of lower b o u n d J - R curves for limited a m o u n t (e.g. 2 m m ) of allowable crack extension seems at present one of the most reasonable methods for dealing with ductile fractures in the upper shelf region. Fatigue crack growth Assessing the integrity of RPVs against consequences of fatigue crack growth ( F C G ) during the whole operating life can in principle be based o n either consideration of subsurface cracks that will p r o p a g a t e in a dry (air) environment, or assumption of surface cracks that will be affected by the p r i m a r y water environment. Indeed, arguments can be found to support b o t h philosophies. A carefully inspected, defect-free cladding is no d o u b t a significant barrier against ingress of water to sub-surface defects: calculations [1] have shown that

under-clad defects 15 m m deep would not p e n e t r a t e a 4 m m cladding layer within the reactor life a n d even greater defects could be tolerated for c o m m o n clad thickness of 5 to 7 mm. O n the o t h e r h a n d sub-surface cracks could penetrate the cladding as consequence of fast p r o p a g a t i o n (with rupture of the clad ligament) during a severe thermal transient or e n v i r o n m e n t a l cracking (e.g. due to faulted water chemistry) of the clad itself may occur. The choice between the two possible conditions is of substantial relevance, since while in the first case (dry crack) F C G analyses can be based on a large a m o u n t of reliable experimental data, in the second case (wet crack) experimental data are less complete a n d sometimes not completely consistent. C o n c e r n i n g dry cracks it is generally agreed that fatigue crack growth up to reactor E O L is of no concern for vessel integrity. F o r example, calculations [1] have shown that a 50 m m deep crack (which is very unlikely at present level fo N D E techniques) at a critical vessel location would grow less t h a n 7 m m d u r i n g the whole operating life. W h e n the relevance of wet cracks has to be assessed the A S M E XI [24] reference curves for surface (wet) cracks (see fig. 10) are currently used. These curves include the effect of the R-ratio (ratio between the m i n i m u m a n d the m a x i m u m stress intensity factor val-

E. Vitale / Structural integrity of RPVs APPLIED CYCLIC STRESSINTENSITY.ksl 10 °

101 I

.......

10 z / I II / ; / 4

. . . . .

lo ~

I

16 3

,','// I//I I///// / / .I]1

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I~ ~ ~°

I

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~ ,,, ==

,

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106

I

,

102

APPLIED CYCLIC STRESS INTENSITY MPa~/m

Fig. 10. ASME Sect. XI reference fatigue crack growth curves for s u b s u r f a c e (dry) and surface (wet) flaws.

ues within a fatigue cycle) and are intended to be an upper bound to laboratory data obtained in both P W R and B W R high temperature water simulated environments. There are however significant experimental evidences that crack growth rates in actual service conditions may remain substantially below the A S M E reference curves, that hence would be overly conservative. Recent detailed re-evaluations [44-48] of experimental F C G data in P W R and B W R environments have led to recognize that a large number of factors, including details of the experimental rigs, can affect the measured crack growth rates, leading either to a negligible or to a significant environmental effect. Trying to give a very brief review of recent findings, we shall consider the following points: 1. The material dependence of F C G is negligible in comparison to other effects. For example, differences between A508 Class 2 and A533B Class 1 steels are non-existent and also weld and H A Z material behave in a very similar way. On the other hand, details of the material chemistry may be very important: it has been recognized that the sulfur content has a strong impact on environmental sensitivity, with higher

83

sulfur content resulting in higher environmental effects. 2. Environmental variables also seem to have a relatively slight effect. Observed crack growth rates in BWR and P W R environments show fairly good agreement under comparable loading conditions. The basic difference between the two environments is the dissolved oxygen content: deoxygenated water is used for PWRs, whereas a constant concentration of oxygen is maintained under B W R conditions. The content in dissolved oxygen should in principle introduce differences in the environmentally assisted crack growth mechanism, but it can be argued that the effective oxygen concentration at the tip of the growing crack is usually very low [47,48], at least for not very high water flow rates. However, faulted water chemistry, particularly in relation to oxygen content, should carefully be avoided in order to prevent surface initiation of stress corrosion cracks. 3. The loading history related variables, such as the cyclic stress intensity range, the R-ratio and the frequency (or "rise time") and waveform of the cycle, have the most pronounced effect on the observed F C G behaviour. In fact, the rate of the environmentally assisted crack extension seems to depend on a balance between the crack tip strain rate, which controls the rupture of the passivating oxide film, and the rate of repassivation. There is a window of frequencies where very high F C G rates, almost independent from mechanical parameters, can be attained relative to an inert environment; above this window (at high frequencies) no time is available for any environmental enhancement of growth rates and mechanical parameters are dominant; below, total repassivation occurs and again environmental sensitivity is low. There are evidences that the extent of this window may depend on details of the electrochemical conditions at the crack tip and hence on water flow rates too. The difficulty in reproducing these kind of conditions has led to a very high scatter of measured crack growth rates (see figs. l l a and l l b ) , and is indeed the more severe obstacle to a conclusive characterization of the phenomenon. 4. Due to the complex dependence of F C G rates on loading history parameters, it is very likely that simple "linear summation" rules, at present currently employed in calculations of crack lengths resulting from variable loading histories, are not adequate to predict crack behaviour under actual service loadings. Experimental data are very scarce in this field and testing with complex waveforms (variable amplitude, variable frequency) is definitely required to

E. Vitale / Structural integri O, of RP Vs

84

-4

lO I CONSTANIS lo-4r 1

R = 0 71 t° 0161 (S:ATTE~B--AND)-

. . L-S ORIENTATION SI NE WAVE FREQUENCY 0 0167 Hz VARIABLES Envi ronment R- 0,2 R=0.5 R=0.7 Li O [] O

~, ' l

2 - R = 024 to 011 (SCATTER BAND)

/~

ALL SPECIMENS 1 cpm SINE WAVE

/

1

165

10~

L, B

~

L i H2 Li B H2

(~ '~

co >-

ld 6

(~

I

16 6

I

CO

CO

I

E

E

l .I I

ASME XI WET [19801 R~065

ASME Xt WET (1980) R~ 0.65

~Z

ld 7

16 7

//

/ / /,

I

(a) . . . . .

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e []

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.

ASME Xl WET _ _ (1980) Rs0 25

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.

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.

.

.

.

.

.

.

.

.

.

.

.

/ I / L,,I

o/

(b)

&t

. . . . . . . .

100

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100

Fig. 11. Comparison of the ASME Sect. XI wet and dry curves with the Westinghouse (a) and UKAEA (b) data on A508-C1 and A533-B steels in PWR simulated environments (from [46]).

investigate material b e h a v i o u r u n d e r more realistic loadings, directly c o m p a r a b l e to RPVs operating conditions. 5. A limited a m o u n t of F C G tests on pre-irradiated materials [47,49,50] in simulated P W R e n v i r o n m e n t s indicates that irradiation does not further increase the growth rates b e y o n d the increase which is due to the e n v i r o n m e n t itself. In conclusion, it c a n be stated that, although present A S M E XI reference curves woud provide conservative crack growth predictions for RPVs in well controlled P W R a n d B W R water environments, they do not seem to be based o n a correct physical model of the environmentally assisted crack growth mechanisms. Since these curves are based o n accelerated laboratory tests, the extrapolation to the lower cyclic frequencies experienced in actual operating conditions is questionable. Recent findings a b o u t strain rate effects on crack growth rates in P W R a n d B W R e n v i r o n m e n t s suggest

that the use of modern, low-sulfur materials a n d p r o p erly controlled water chemistry m a y prevent the onset of the electrochemically controlled cracking process. Benefits of such a c o n d i t i o n can be for example deduced from the g r a p h of fig. 12, which shows the effect of the lower frequency (or crack tip strain rate) threshold (for the onset of e n v i r o n m e n t a l l y controlled cracking) o n the calculated crack extension at EOL, for typical P W R conditions a n d loading history [46]. It can b e seen that for threshold values above - 2 × 1 0 - 4 s - 1 the a m o u n t of F C G is negligible, while below this value a n d at - 3 x 10 -5 s -1 s u d d e n increases of crack extension are predicted, since a larger part of the transients in the P W R specification comes in the frequency w i n d o w of electrochemically controlled growth. If the physical m e c h a n i s m s of the p h e n o m e n o n will b e better u n d e r s t o o d a n d this philosophy can be further developed, then a possible code a p p r o a c h could b e to deal with p u r e fatigue only, with specific instructions on

E. Vitale / Structural integrity of RPl/s 50

40

r..o o~

ASSUMPTIONS : I N I T I A L CRACK

>,-

DEPTH = 25 mm

o

30

ASPECT RATIO, 6:'1

Z

E "r

2o

o CJ

10

d •"lO-11&K3m/cyOe = 4 and ASME Xl [19801 equations gwe same result ~ =6'5x104

i 10-3

I 10 -4

I 10-5

10-6

THRESHOLD [ sec-1]

Fig. 12. Calculated crack extension in the cylindrical section of a typical PWR vessel, as function of the treshold strain rate for the onset environmentally controlled crack growth (from [46]).

the metallurgical and environment parameters which would prevent the onset of environmental interaction [46].

100 UNIRRADIATE D

80

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-

,

>- 6O ~

~

O

////~

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=

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100

200

85

Cladding effects Consideration of the effects of the internal clad layer, typically an approximately 5 mm thick, weld-deposited layer of type 308 stainless steel, is at present very poor in RPV structural integrity assessments. The benefit deriving from impedance to heat transfer to the inner ferritic material is currently accounted for, but structural effects, which can arise in a variety of ways, are generally ignored. Concerning the behaviour of cracks at the clad-wall interface, it is argued that a tough clad material may have the capability of restraining the opening of cracks, thus improving resistance to crack initiation and preventing short cracks from growing circumferentially or longitudinally becoming "long" cracks (see section 2.3). Accounting for such effects would require a detailed knowledge of the toughness of clad materials and of their sensitivity to neutron irradiation. Recent investigations at the O.R.N.L. [32] have shown that specimens machined from a typical type 308 cladding, irradiated at a temperature and fluence similar to those at the EOL for a PWR vessel, exhibit very little degradation of the notch-impact toughness (see fig. 13), thus confirming the possibility of significant beneficial effects on vessel integrity. Other significant clad evaluation programs are being carried out [51,52], both for characterization of clad properties and for the assessment of the role of cladding in preventing crack propagation under severe thermal and pressure loading. Preliminary tests on cracked 4-point bending specimens with and without cladding [51] have shown that a relatively low-toughness stainless steel cladding has a limited capacity to arrest a running crack on the surface and keep a short crack from becoming long. If confirmed, these results will indicate that beneficial clad effects may eventually be considered, provided that demonstration of high cladding toughness after exposure to service conditions can be achieved. At present, it has however to be recognized that published data on clad fracture properties are still too limited, so that accounting for favorable clad effects would not be justified in the framework of conservative vessel integrity evaluations. For this reason treatment of cladding effects will not be dealt with in the following sections, concerning analytical models, even if advanced methods for including them in facture mechanics analyses have already been proposed [53,54]. 2.3. Crack shape and dimensions

400

(°C)

Fig. 13. Effect of irradiation on the Charpy impact energy of type 308 stainless steel cladding (from [51]).

In comparison to the extreme variety of shapes, dimensions and orientations that actual cracks may have, only very simple classes of defects are generally

86

E. Vitale / Structural integri(v of RP V~

assumed in fracture analysis of RPVs. This is done in order to avoid excessive complexity (and related uncertainties) and because it is possible to obtain a great simplification by reasonably conservative assumptions. In performing acceptability analyses of detected flaws, the problem is to translate actual shapes and orientations into simplified cracks, amenable for F M analysis; in doing such kind of approximation the Appendix A of A S M E XI [24] does provide a useful guideline. At a design stage, defects have to be postulated at vessel critical locations characterized by either stress concentrations or degradation of material properties. Important penetrations, such as those for the control rod drive mechanisms and the inlet and outlet nozzles, the flange region and welded joints may all be very sensitive to the presence of crack-like defects and, of course, a particular attention has to be p a i d to critical locations (welds, stress concentrations, etc.) in the beltline region, since it is subjected to the highest level of neutron irradiation. It is clear that much of the conservatism of the fracture assessment depends on the assumed crack shape and dimension at each location. In establishing pressure/temperature limits for normal and upset loads, Appendix G of A S M E Section IlI specifies a 1 / 4 wall flaw of 6 : 1 aspect (length to depth) ratio; on the other hand, little guidance is provided concerning flaws to be used for emergency and faulted conditions. A conservative basis for establishing defects to be postulated for accidental thermal transient analyses is to consider the main welds that join the sections from which a PWR vessel may be fabricated. Cracks in the most critical beltline welds are generally assumed to be two-dimensional: infinitely long axial cracks and continuous circumferential cracks for plate-type vessels, which have both axial and circumferential welds, and continuous circumferential cracks for vessels fabricated from ring forgings. For plate-type vessels long axial cracks tend to be of greatest concern since the stress intensity factor can be substantially greater than for circumferential cracks. Notwithstanding the extreme simplification that is associated to these assumptions, there are several reasons that make them quite acceptable: two-dimensional cracks can be very simply and accurately treated in F M analyses; - the more probable finite-size flaws are much more difficult and expensive to analyze; - there are indications that under thermal shock load-

ings short surface flaws would grow to become long flaws; - assumption of long cracks seems a reasonably conservative approach. Surface semi-elliptical cracks, with various aspect ratios, are usually considered for analysis of both fatigue growth and crack initiation in regions with stress concentrations (nozzles, flanges, etc.); sometimes semielliptical flaws are also assumed in the beltline welds, in order to study less conservative conditions for first initiation during thermal transients. For plate-type vessels it has recently been proved [55] that considering infinitely long axial defects may be overly conservative. In fact, the axial welds of adjacent shell courses are staggered, so that the length of a continuous axial weld is no greater than the height of the shell course. If the concentration of copper in the weld is high compared to that in the base material (as normally is the case) it is not likely that crack propagation will extend outside of the weld region. Thus, the maximum length of the crack will be no greater than the height of a shell course, which is approximately 2 meters. Calculations show that stress intensity factors for these 2-meters flaws may be significantly lower than

CROSS

r

S E C T I O N OF R P V T H R O U G H

CO~E

¢

~I~

AX~AL WEt~

©

,1 ¢ Fig. 14. Schematic diagram of typical azimuthal fluence variation in the beltline region of a plate-type PWR vessel (from [551).

E. Vitale / Structural integrity of RPVs

those of the infinitely long flaws of the same depth [55]. As a consequence, the most reasonable scenario for the study of accidental transients would be that of a reasonably likely semi-elliptical surface defect (e.g. the 6 : 1 , 1 inch deep flaw) at the vessel inner wall, which first propagates in the axial direction, becoming a 2-meters flaw, and then continues in the radial direction, having an increased tendency to arrest in comparison of the infinitely long axial crack. Similarly, there are arguments for imposing limits on the length of circumferential cracks, which would be of great relevance for forging-type vessels. In fact, the azimuthal variation of the neutron fluence, of which a typical example is shown in fig. 14 [55], should limit the propagation of cracks to the most embrittled regions of a circumferential weld. However, consideration of this effect would make the problem very plant-specific, besides introducing a considerable number of uncertainties, so that considering continuous circumferential cracks, at least after the first initiation event, appears at present to be a reasonably conservative practice.

3. Analytical fracture models Depending on whether a ductile or brittle fracture behaviour is expected as a function of loading conditions and estimated material properties, L E F M or E P F M methodologies should be applied, eventually coupled with more conventional design methods. While L E F M criteria and procedures are at present in a well assessed state, and only a few particular aspects need some further improvements, E P F M is still in a developing stage and several alternate methods are being evaluated for characterization of ductile crack initiation and growth. In the following, current L E F M methods will be reviewed with reference to critical aspects related to RPV analysis. Concerning EPFM, a couple of proposed methods, at present judged to be among the more suitable for practical application, will be discussed, with no attempt to give a complete review of E P F M approaches, about which ample discussion can be found in the literature [43,56-58]. Design methods for evaluating fatigue crack growth are presently based almost exclusively on the very straightforward application of the Paris law or on modifications of it [59,60], and will not be further discussed for the sake of brevity. In some cases reference will be made to more conventional design methods, such as yielding criteria and plastic collapse analysis, whose procedures are not herein reviewed.

87

3.1. L E F M methods

The basic criteria of the classical L E F M approach can be summarized by the following statements: - a crack will propagate when the applied stress intensity factor, K l, exceeds the material fracture toughness, K~c, at the current temperature; - a propagating crack will be stopped when the current Ka becomes lower than the arrest toughness Kia. An alternative to this i n i t i a t i o n / a r r e s t analysis is the Nil-Ductility Temperature ( N D T ) approach of Pellini [61], which simply defines a minimum allowable service temperature, for low strength ferritic steels with yield stress in excess of 50 ksi (344 MPa), as function of the operating stress level and material RTND T. Although the method is a very useful engineering guide to the prevention of brittle farcture and it has actually been employed as screening criterion for RPVs acceptability analyses, it has a number of evident limitations for the evaluation of thermal transients, where high stress and temperature gradients are present in the vessel wall. As already outlined, the maximum risk for a postulated or detected flaw to propagate in the vessel wall occurs in response to severe thermal transients with high system pressure and in presence of pronounced irradiation-induced material embrittlement. In such a scenario the typical condition at a generic location in the vessel is that depicted in fig. 15, with steep stress and temperature gradients across the wall thickness. Pressure and thermal stresses are typically biaxial so that both longitudinal and circumferential cracks are considered to be subjected to pure mode I opening and stress intensity factors K l are used in the analysis. Even if more complex situations can obviously occur in actual RPVs, this simplification, coupled with the pessimistic assumptions (see section 2.3) about flaw shape and dimension, is thought to be reasonably conservative. A typical distribution of K I, Kic and Kxa along the vessel wall thickness, at a particular instant during a severe thermal transient, is shown in fig. 16. Here, Kit and Kla are evaluated as functions of the temperature and taking into account the irradiation-induced shift of RTNDT, computed according to methods described in section 2.2. Due to the combined effect of temperature and fluence gradients fracture toughness gradients in RPV walls are often found to be extremely steep. In order to analyze with one graph all of the failure conditions that may happen during a given transient we can plot, as it is shown in fig. 17a (representing a typical PTS transient), critical crack depths (i.e. crack lengths for which K 1 = K l c or K l = Kla ) as function of time

88

E. tqtale / Structural integri(v o f R P l ~ , Ro = 246 m

{

1

..... 7 - - T

. . . .

400 TIME=

KIc

IATION

160 sec

;I

.

Uq

350

300

sol-,

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ooL

"

[ 150 ~ _ ~ 1

0

100 ~_

02 04 06 08 a,'w FRACII()NAL WALl AN[) FLAW D[PTH

!

0

Fig. 16. Distribution of fracture-mechanics parameters through the wall of a PWR vessel at a given instant during a large break LOCA (from [25]). Ri= 2,3m I

I

I

I

I

I

~

I ^l, cmL

Fig. 15. Typical pressure and thermal stress distributions through the vessel wall.

arrest

wPs I

~ K

I =KI a

S

£

from the beginning of the transient. It is seen that an initially short flaw has the possibility to propagate and arrest several times during the transient, penetrating deeply into the wall of the vessel. When the only relevant stresses are those of thermal origin (low pressure transients, such as large break LOCAs) the

te

_max:_penetra~on_

JE

go.

go t~

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l

--

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(a) ~ 20

0

K

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I

=

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20

Fig. 17. Schematic Critical Crack Depth (CCD) diagrams for typical PTS (a) and TS (b) conditions. It is shown that during PTS a crack could propagate very deeply in the vessel wall, at least in conditions where Warm Pre-Stressing (WPS) were not active.

E. Vitale / Structural integrity of RPVs

08 K~C

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WPS)

89

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,

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Fig. 18. Schematic diagram of Warm Pre-Stressing (WPS) with three load/temperature paths.

/

0 - - 1 1

0.1

- -- - - "=" - ~ " ~ " - F

o critical-crack-depth curves tend to flatten (at least for less severe transients), as schematically shown in fig. 17b, with the consequence that a) defects deeper than a certain value will not start propagation and b) propagating defects will not be able to penetrate through the entire wall thickness. There is a large and consistent amount of experimental data [62-64] confirming the capability of residual compressive stresses, generated by application and removal of an high stress intensity factor at upper shelf temperatures, to prevent or retard crack initiation upon re-loading (see fig. 18). This effect, known as W a r m

- -

I RST I N I T I A T I O N

l

I

1

2

L 3

L

I

l

1

4

5

6

7

TIME (rnin)

Fig. 20. Critical Crack Depth diagram for the O.R.N.L. TSE-5A Thermal Shock test on a large-scale cylinder with a long axial crack (from [26]).

Pre-Stressing (WPS), has a great potential to reduce the risk of RPV failure during thermal transients, since in many cases the crack tip will be cooled as to exhibit a brittle behaviour well after that the applied stress intensity factor has reached its maximum value.

150

100

+

EXPERIMENTAL

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-160

I

-140

I

I

-120

-100

-80

-60

I

-40

I

-20

I

0

20

TEMPERATURE (°C) Fig. 19. Comparison of experimental and predicted fracture toughness after WPS at about 20°C (from [66]).

90

E. Vitale / Structural integri!v of RP Vs

5°°] I~oo I ~Ill I ,./[I [ I 1 t 450

#

~

INITIATION

/

t 350

--

ARREST

/

l

/

"'~"~'~

C R A C K JUMP

.......

Klc

300

~- 25o a/w • 0 1 6 5

~- 200

15O

1O0

50 I +

I So

I

1 1O0

I

[

I

1

150 200 C ; I A C K TIP T £ M P E f ~ A T U H E

1

.1 250

N ~00

PICI

Fig. 21. Initiation and arrest toughness data from the O.R.N.L. PTSE-1 (A,B,C) Pressurized Thermal Shock test, compared with reference toughness curves form tests on standard specimens (from [31]).

Prediction of the effective K I a t initiation, after a given degree of WPS, can be based on the evaluation of the crack-tip residual stress field as function of the maximum applied stress intensity factor, K~,~x, and of the actual load-temperature history [65,66]. As an example, fig. 19 shows a comparison of results from WPS experiments with toughness predictions based on a local fracture criterion [66]; it is seen that the agreement is quite good and that crack initiation is not predicted until Kt reaches the new effective toughness boundary generated by prior loading. Recent validation experiments [25,30,67] have demonstrated the effectiveness of the above described methodology in predicting the behaviour of cracks in heavy section reactor materials under both pure thermal loads (see fig. 20) and typical PTS conditions (see fig. 21). In particular, several critical questions concerning the application procedures have received convincing and well documented answers; among these, fundamental points that must be outlined are the following: (a) application of fracture toughness values derived from tests on standard specimens to RPV analysis is a sound procedure, provided that statistical treatment of data is used to derive reliable lower b o u n d toughness curves;

(b) the same conclusion applies to arrest toughness, even with the limitations, outlined in section 2.2, due to imcompleteness of material characterization in the transition and upper shelf regions: (c) successful predictions of crack arrest in typical RPV conditions can be obtained using static analysis, dynamic influences being neghgible in most cases (generally, when very long crack j u m p s can be excluded); (d) WPS is effective in preventing crack propagation or re-initiation, at least in cases of " s i m p l e " WPS, that is under conditions of decreasing stress intensity factor (excluding reloading). However, when these L E F M calculations have to be applied in actual design or for acceptability analyses, the great number of required inputs (for material properties, flaw distribution, stress calculations, etc.) and the variety of loading conditions that have to be examined, raise the question of which is the correct philosophy to employ. A complete review of the implications of Code requirements a n d / o r regulatory positions will require so much space that it is out of the scope of this paper; nevertheless it seems useful to outline some critical points. A first point concerns the choice of input parameter values. The general approach used in regulatory calculations is to choose conservative values for each input. An alternative approach could be to use " b e s t estimate" values for each input and impose a final safety margin to the result. Both of the methods have shortcomings and advantages but in general the final level of conservatism will be ill-defined and the more complex the calculation the greater the conservatism (for the first) or the uncertainty (for the second) which results. Methods which allow for a quantitative estimation of conservatism are discussed in section 4. A second point is the value of the nominal safety factor to be required for each loading condition. While for normal and upset conditions safety margins are explicitly accounted for (at least relative to primary loads), for severe thermal transients, which can be classified as "emergency" or " f a u l t e d " loads, no safety factors are used in fracture assessments. In these cases the conservatism of the analyses depends on the use of realistic upper bounds on postulated flaw sizes and predicted irradiation-induced shifts in RTND.r, since lower bound curves for Kic and Kla may not offer any degree of conservatism, as discussed before. A third point concerns the treatment of stresses. Both primary and secondary thermal and local stresses are currently combined for estimating the applied K I levels, while residual stresses are often neglected, con-

E. Vitale / Structural integrity of RP Vs

-

sidering that their effect is accounted for by the general conservatism. This may not always be a sound procedure and indeed further research is urged on the levels of these stresses and on accurate methods of including them in fracture analyses. Finally limitations due to actual geometry and loadings should be taken into account. As examples, it seems worth sketching the followings situations: - for a deep crack in a vessel under pressure the crack-tip plastic zone size can be so large that L E F M no longer applies and E P F M methods have to be used; furthermore, with pressures at a significant fraction of the design pressure, the possibility that the net ligament fails by plastic instability should be considered; notwithstanding the positive outcome of validation tests, extreme care should be used in including the beneficial effect of even " s i m p l e " WPS in engineering safety analyses, where the detailed conditions of loading are subjected to noticeable uncertainty; for instance, plant records show that pressure fluctuations may occur during cooling transients, and these fluctuations could negate the condition of decreasing K~ from a decaying thermal stress field; furthermore, in certain cases the K I level decreases only slowly and never falls substantially below its peak value, so that small changes in the pressure/temperature history would negate the WPS condition.

3.2. E P F M methods As already outlined in section 2.2, among the numerous parameters that have been proposed in E P F M the Rice's J-integral is certainly one of the most promising and widely used. When the plastic zone at the tip of a crack grows to a size that is no longer negligible in comparison to crack depth or remaining ligament, the elastically calculated stress intensity factor no longer repesents the effective condition of the material at the crack-tip, which determines the possibility of crack propagation or stable growth. There is consistent evidence that characterization of both crack initiation and growth in an elastic-plastic crack-tip field can be obtained by the J-integral, at least for a limited amount of crack extension. This approach has, besides all, the advantage of being perfectly equivalent, in purely elastic conditions, to the classical L E F M method, through the well-known relation between K and J (which for mode I writes: Jl = K I2/ E , , where E ' = Young modulus ( E ) for plane stress and E ' = E / ( 1 u 2) for plane strain conditions).

91

Application of Rice's integral to typical RPV loading conditions require an extension of its original formulation in order to include the effects of thermal strains. Such an extension has been proved to be feasible and practical (e.g. by calculation of an area integral besides the usual contour integral) by many authors [68-71]. The J-approach (also called the J - R curve approach) states that a crack starts growing when the applied J~ equals the material resistance to crack initiation, Jlc (in elastic fields: Jic = K i cE/ 2 ,). During ductile cracking, an increasing resistance to crack extension is generally observed after initiation, so that stable growth may occur, the condition being that the crack-driving force (i.e. the applied J, Jappl) equals the material resistance Jg(z~a), function of the amount of crack extension (Aa). This will require an increase of the applied loads, thus enhancing the limits of safe operation of the component. The maximum amount of stable growth can be predicted from the condition of tangency between the Jappl and the JR curve, the condition for onset of unstable growth being:

()Jappl

~)JR

- 3a - > -- - 3a .

(1)

Of course, limits for J-controlled crack growth a n d / o r plastic collapse should not be overcome for this criterion to be valid. A relatively recent methodology, which can virtually take into account all of the possible failure mechanisms in RPVs, is that based on the so called Two Criteria Approach, initially formulated by Dowling and Townley [72], and its various modifications and improvements, such as the C E G B R6 method [73] and the E P R I engineering approach [74,75]. In the most general formulation a Failure Assessment Diagram ( F A D ) is employed, with coordinates (St, K r) defined as: Sr(a o + Aa) = o/o,( a o + Aa), Kr(ao+Aa)=~-J,E(ao+Aa,

(2) e)/Ju(Aa),

(3)

where: a 0 is the initial crack depth, A a is the amount of stable growth. o is the applied stress on the structure, o 1 is the plastic collapse stress based on the material flow (or yield) stress, JiE(a0 + A a , P ) = K 2 ( a o + Aa, P ) / E " is the elastically calculated value of Jj. For crack initiation Aa = 0 and J R ( A a ) = Jlc. For a particular stress level and initial flaw size the coordi-

E. Vitale / Structural integrt O' of RPb]s

92

1,0 0,8 O~

Failure assessmentcurve(O.O(a/t <.25) for typical reactor vessel steels . . . . . basedupon 6yield'6OKSl[planestrata]

C ~'%B

Kr .'~' S, / /

O2

"

Factor of safety = (U'O*OC) (O0.OA)

~

O'Krl)/

Q // I Q2 0", (0 - K'rS)

I~ I

[

J

I

04

0.6

0.8

10

_

l

12

" I

14

1.6

[

lJ]

20

-02L Sr Fig. 22. Use of the Failure Assessment Diagram (FAD) for the evaluation of safety margins against crack initiation or onset of instability, in cases of primary loads only (dashed line) and primary plus secondary loads (solid line) (from [76]).

hates ( S r, Kr) can be calculated and, if the point lies inside the failure assessment line, the structure will not fail. Since both S r and K r are directly proportional to the applied load, the position of the assessment point relative to the failure assessment curve determines how close the structure is to crack initiation. With reference to fig. 22 the assessment point A will move radially, on increasing the applied load, up to the initiation point, C. When ductile cracking is expected, the method can be extended to account for stable crack growth; in this case the locus of points (St, Kr) will follow the failure assessment line till the maximum load point I, defining the condition of unstable growth. Methods for deriving failure assessment curves are illustrated in [76]. These curves will in general depend upon both material and geometry (particularly, on relative crack size) and should be derived for each specific case. However, it is possible to derive lower bound conservative curves of general validity for usual RPV geometries and materials, as shown by Bloom in [76]. The safety margin with respect to the onset of crack growth can easily be calculated as ratio of e.g. segments OC and OA in fig. 22 and a similar procedure can be used to evaluate margins against final instability or a certain amount of stable growth. In addition, the contribution of pressure and thermal stresses can be separately handled, by posing [77]: K r = --rKP. . . . . . . st=so

....... .

+ -'r/(th . . . . 1 ,

order to obtain the safety factor O ' B / O ' A , intended as the ratio of the primary load to cause failure (or crack initiation) to the primary applied load. For the sake of brevity other details of the application procedure are not discussed here; however, several examples of application of either the described method as it is, or of modified versions can be found in the literature [76 78].

(4) (5)

In this case the assessment origin has to be taken at point O ' of coordinates (0, __~Ktherr""l~,(see fig. 22) in

4. Probabilistic methodology All of the above reviewed methods, irrespective of whether a "best estimate" or " l o w e r b o u n d " philosophy is followed, are based on the classical deterministic design approach of interposing a safety factor between the applied loads and the available strength, in order to account for variabilities and uncertainties that exist in the evaluation of both loads and strengths. The stringent safety requirements on nuclear components, and particularly on RPVs, coupled with the extreme weight of the economical aspect and the complexity of the design problem itself, have given rise to an increasing interest in a better assessment of structural reliability, possibly showing in a quantitative way the influence of variabilities of the basic parameters. Recent works have shown that these objectives can be achieved by means of probabilistic failure analyses and that these methodologies allow cost-effective decision making about design, plant operation procedures and acceptability of old-design components, besides complying to the recent tendency for estimating the probability of catastrophic nuclear accidents by a general Probablistic Risk Assessment (PRA). Since the early studies on reliability of RPVs [29] a very large amount of work has been done in this field and at present several design procedures and computer codes exist which allow for the evaluation of failure probabilities in nuclear components. In the following, basic principles and critical points of most used methodologies for nuclear applications will be briefly reviewed. 4.1. Methods for probabilistic analyses

Reliability of a specific component can in principle be determined by either direct statistical analysis of failure data or indirect probabilistic analysis. The first method, which assumes that the failure probability is given by the number of failures divided by the total number of homogeneous operating components, is very simple but has severe shortcomings for application to

E. Vitale / Structural integrity of RP Vs nuclear pressure vessels: its is generally necessary to group failure data, thus neglecting differences in design, materials, etc.; - as a consequence, it is not possible to indicate all of the factors to which failure probabilities are sensitive; - finally, even for very rough data grouping, failure data may be very few or none, so that the true failure probability can be significantly different from that resulting from historical data. The indirect approach does not require historical failure data but is based on the understanding and modelling of failure modes and statistical distributions of the controlling parameters. By this way the effects of different materials, fabrication processes, design criteria, N D E methods, etc. can be separately assessed. The main disadvantage of this method is that the mathematical models that are used may not accurately reproduce actual variabilities, thus leading to wrong failure probabilities; in addition, validation by comparison with direct historical data is almost impossible for applications to nuclear vessels. In spite of these limitations, the indirect approach is presently recognized as the only method which can provide general and detailed studies of RPV structural relability. However, at the present status of mathematical modelling and understanding of the statistical distributions of the controlling parameters, results of indrect probabilistic analyses should not be taken in an absolute sense (i.e. as a measure of the true failure probability) but rather as useful means for comparing the impact of the different parameters and of possible new developments in design, manufacturing, control and operation procedures. There are two possible ways to apply the indirect method: (a) by a full mathematical solution; (b) by a numerical Monte Carlo simulation procedure. Briefly, the full mathematical solution may be found by expressing the failure condition: -

r ( X ) = L ( X ) - S ( X ) < O,

The exact integration of eq. (7) is possible only for very limited cases so that the method cannot be extended to the complete treatment of generic reliability problems. Nevertheless several solutions have been proposed which are applicable to specific kinds of RPV reliability analyses. Reviews of these methods can be found in [79,80]. The most versatile approach is the Monte Carlo simulation technique, which is indeed widely used in structural reliability assessments. The simulation procedure, which can be regarded as either a numerical way of computing the integral (7) or as a numerical simulation of the actual failure phenomenon, essentially consists of the following steps: (1) generate random numbers, one for each of the variables x,; (2) generate a random point (x 1, x 2 . . . . . xn) according to the probability density function of each variable (this corresponds to generate a random vessel, with random loadings); (3) check if the random vessel will fail or survive (in other words, if the random point falls within the failure domain); (4) count the number of times ( N f) that the random vessel fails and the total number (N-r) of trials (generated vessels); (5) compute the probability of failure as N f / N T. This procedure is so general that it can be applied to virtually any reliability problem, the only shortcoming being the required computing time. In fact, the lower the probability that has to be computed, the larger the number of trials that are necessary to obtain a satisfactory result. For very low failure probabilities (10 6 to 10 -8 or less, as it is typically the case for RPVs), the required number of trials may be extremely high, as to become a serious limitation to the method, due to the high computing cost. For this reason error reducing techniques, such as the " i m p o r t a n c e sampling" and the "stratificated sampling" are generally employed in nuclear applications [79,81-84].

(6)

where r ( X ) is the "failure function", X is the vector of the basic independent variables x~ and L ( X ) and S ( X ) are respectively the load and strength parameters, and calculating the probability of failure, Pf, as:

Pf = P{ r( X ) <_O} = f f x ( X ) "d X ,

93

(7)

where f x ( X ) is the joint probability density function of the variables x i and J2 is the failure domain were the failure condition is satisfied.

4.2. Evaluation of failure risk in RPVs As discussed in the preceding sections, the study of RPV structural integrity depends mainly on the possible behaviour of crack-like defects under a very large number of loading conditions, the most severe of which are some classes of accidental thermal transients. The problem of computing the actual vessel reliability ( 1 probability of failure) can be therefore seen as the problem of determining the "conditional" probability

94

E. Vitale / Structural integrity of RPVs

of crack extension, P f ( C E / ~ ) , (with or without considering arrest, stable growth, etc.), given that a certain transient, ~ , does occur. The probability for this transient to occur P(T,) can be calculated from reliability analyses of plant components and event-tree studies, so that the total failure probability Pf(CE) for all of the N T considered transients may be finally computed as: NT

p~(CE) = Z &(CE/~)-p(V,).

(8)

i--l

The conditional probability of RPV failure can be calculated by Monte Carlo simulation given that the probability density functions of the controlling parameters are known. Referring to the L E F M methods discussed in section 3.1, a complete reliability analysis would require simulation of the statistical distributions of a least the following parameters: - crack shape, size and location, - initial RTNDT, - irradiation fluence at the inner vessel surface, copper and nickel contents, - irradiation shift, ARTNoT, initiation toughness, Ktc, - arrest toughness, Eta. Once a random set of parameters has been generated, the fracture analysis is performed in a deterministic way, by the already described methods, so that the accuracy of the method is fundamentally dependent on the accuracy of models employed for simulation of distributions of parameter values. Computer programs developed for TS and PTS probabilistic analyses generally simulate both crack initiation and crack arrest events, and associate vessel failure only to deep crack penetration through the wall thickness or onset of plastic instability. Detailed descriptions of some of these codes can be found in [83-87], It seems herein useful to give an overview of problems related to the statistical simulation of critical parameters (particularly, crack size and location) and finally show some examples of probabilistic analyses. Distribution of cracks In terms of its effect on the calculated probability of failure, the distribution of cracks is one of the most important parameters. Unfortunately enough, there is at present a considerable uncertainty associated with possible crack distributions. First, there is the question of how many dimensions

are necessary to adequately describe a flaw. It would be enormously complex to try a complete probabilistic description of crack shape, size, depth and orientation; therefore, the present practice is to consider mode I, surface breaking cracks characterized by either one (the depth for either long cracks or elliptical cracks with given aspect ratio) or two (depth and aspect ratio) dimensions. A second problem concerns the difficulty of obtaining probability density functions even for crack depths only. The probability for a certain crack to exist in a RPV during operation depends on the manufacturing process and on the reliability of N D E techniques that were employed for pre-service inspection (Probability of Detection: POD). The POD depends on size, orientation and location of flaws and also varies for different N D E techniques and inspection teams [2,88]. Finally it must be considered that crack distributions may differ by material and location; e.g. the size distribution is generally found to be different in Heat Affected Zone (HAZ), weld and base plate or forging materials. A commonly used way to obtain the crack-depth probability density function is to multiply the crack-depth density function prior to pre-service inspection, f ( a ) , by the probability of non detection of cracks ( 1 POD), B(a), associated with the final in-service inspection, assuming that any detected flaw is repaired. Then, assuming that all cracks of interest are located in the welds, the final probability function is:

P(aai) =NVf

f(a)B(a)da,

*'Aa~

(9)

where: fraction of cracks with depths in the range a - a + da, (number of cracks in the range a-a + da B(a) when vessel goes into s e r v i c e ) / ( n u m b e r of cracks in the range a - a + da prior to repairs), P ( A a i ) = number of cracks in weld material having depths in the range (Aa D, as the vessel goes into service, N = number of cracks of all sizes per unit volume of weld material, prior to pre-service inspection, volume of weld material, V Aa; = range of crack depths about a~ such that ~ A a , = wall thickness.

f(a)

E. Vitale / Structural integrity of RPVs Other variables

If we define:

A,=

fa~f(a)B(a)da/fo~f(a)B(a)da,

(10)

i

Bi=EA

95

,

(11)

!

then, flaw depths can be selected by generating random numbers between 0 and 1 and comparing them with B i values (i = 1, n): the simulated flaw depth is that which corresponds to the smallest value of B i that is greater than the random number. The function f ( a ) and the value of N have to be derived from manufacturers' data and experience, while the function B ( a ) should be based on the analysis of N D E experiments. Various estimates exist for the number of defects per cubic metre of weld (sometimes, per vessel or per metre of weld), currently employed values ranging from about 2 to about 6 defects per cubic metre [89]. Experimental data to support an accurate description of functions f ( a ) and B(a) in a RPV are very difficult to obtain and indeed the presently available data base is not satisfactory. Early estimations presented in the Marshall report [29] are still currently used and recognized as the most soundly and conservatively derived from experimental data. However, results of several experimental programs are at present becoming available [2,88-90], showing that a very high confidence of N D E techniques can be reached by high qualification of personnel and procedures. Fig. 23 shows the comparison of the B ( a ) function proposed in the Marshall report and some recent results obtained by U.K. detection teams [89].

Distributions of other independent variables, such as material initial RTND T, chemical composition (i.e., nickel and copper contents), inner wall fluence, initiation and arrest toughness, are usually assumed to be normal, so that they are described by mean values and amplitudes of standard deviations. The correct way of handling these variables in the simulation procedure is not always obvious and significant differences in the final calculated probabilities may result from different assumptions. Just to mention a few of the problems which have to be faced, we may remember the following aspects: - the choice of independent variables is not always obvious; for example, the irradiation-induced temperature shift, A RTNDT, may be considered as either an independent random variable or a deterministic variable, depending on random generated values of fluence, chemistry, etc. [85]; initiation and arrest toughness values may be considered as either totally independent or having some degree of correlation, such that if, for example, KI¢ at the tip of a crack is 0.5 standard deviations above the mean, then Kla will also be 0.5 standard deviations above its mean value; - distributions of variables have often to be truncated either at some given value to avoid physically unacceptable values (e.g. negative fluence or copper content), or at a given number of standard deviations to avoid unrealistic values and to limit computing time. Additional details concerning procedures for simulating failures of cracked components can be found in [83-85,91]. -

Examples of application

1 o.a

0.6

\~

- - M a r s h a l l B (a) w Prop_osed f u n c t i o n of Cameron[89]

ew0.2°4~,~\ o-<

2s

3'0 a ~ - , o

,s

a (mm)

Fig. 23. B(a) function proposed in the Marshall report [29] compared with B(a) extimations from U.K. teams and a new proposed function (from [89]).

Probabilistic methodologies have widely been applied to evaluate the structural reliability of RPVs, both in plant-specific analyses [92-94] and in general assessment studies [89,95,96]. Also available are examples of probabilistic E P F M analyses [89,97,98]. Fig. 24 shows the results of a probabilistic analysis focused to determine the transient scenarios that dominate a plant's total PTS risk [96]. Several kinds of " t y p i c a l " thermal transients have been selected and probability of their occurrence has been derived by an event-tree approach; then, conditional failure probabilities have been evaluated as function of the adjusted EOL surface RTND T and finally failure frequency per reactor operating year has been obtained for each transient. The total failure frequency is simply the sum of contributions from all of the transients. Once a

96

E. Vitale / Structural integrity of RP Vs b

c e~

03 ~ o ~

LOCA Lo~,o~Coo4,.~*c,..~.,,, P~ss,,.,y Go.,

u.c,

SSB*~

,~

;i//Z >. o"

~.~

ic

c

oT

i"//

100

150 200 250 Mean Surface RTND T (OF)

Fig. 24. Extimations of vessel failure frequency for several accidental transients, as function of the RTNDT at the inner wall of the vessel (from [96]).

certain "PTS Safety Goal" (i.e., a certain maximum acceptable failure probability), P', has been established, the graph of fig. 24 can be used to choose the transient of greatest interest (LOCA "B" and SSB "A") to be used for more detailed or plant-specific analysis. Also, the very low risk transients can be eliminated from

further consideration. Conditional failure probabilities due to a large LOCA transient are plotted in figs. 25a and 25b as function of the vessel operating time [89]. Here, upper shelf material behaviour has been assumed and failure probabilities have been computed in correspondence of either crack initiation or 2 m m stable crack growth, calculated along with the J-R curve procedure (see section 3.2). It is shown that the failure probability increases significantly from semi-circular to semi-elliptical and to extended crack shapes and that allowing for limited crack extension can decrease failure probabilities up to two order of magnitude. The effect of assuming different efficiencies of N D E techniques is evidenced by comparison of fig. 25a and fig. 25b: the use of an improved function B(a), derived on the basis of inspection data generated in the U.K., can greatly reduce the failure probability deriving from extended (long) defects. A probabilistic assessment of pressure/temperature allowable limits is shown in fig. 26 (from [79]), where constant failure rate curves are plotted for a vessel at his EOL (maximum irradiation-induced embrittlement). The figure also shows the operational pressure-temperature limits specified by the A S M E Code [24], for which less than 10 7 failures per transient are predicted.

KEY

All extended

10-I

INITIATION

10 I

_ __ F

--J m

INITIAT ~ON

10-~

. . . . . .

......

102 1

a.

--'--

defects

All s e m i - elhptica~ d e f e c t s All semi- c i r c u l a r d e f e c t s

GROWTH (A533-B) "'='~F[I~ION

~ "-"

STABLE

----" ~ u~ ._1 u.

10-3

Z

10-4

O

KEY

All extended

______

All semi-elliptical

--'--

A l l semi- c i r c u l a r defects

~STABLE

[ 10 3 b--

INiTiATION

. . . .

defects defects

GROWTH tA50B-3)

10-4

AFTER 2rnmGROWTHtA533-B/

10-5

AFTER 2ram GROWTH{A533-B)

- - ____

AFTER 2mm GROWTH(A533-B/

.~-

STABLE GROWTH tA533-BI

,.-,, Z O

I 0-5

10-6

sTABLE GROWTH [A_A~533-B).._~_.

I

I

I

10

20

30

TIME Fig.

25.

(years)

(a)

"

I 40

10,6

I

f

I

10

20

30

TIME

(b)

J 40

(years)

Conditional probabilities of crack initiation and of exceeding 2 mm stable growth during a large break LOCA, using the Marshall (a) and the Cameron ( b ) B(a) functions (from [ 8 9 ] ) .

97

E. Vitale / Structural integrity of RPVs 2500

"///

2000

// / / //// '--~/ / .

UJ

g ,o

10"~Failures per Event~ \ O'F+,,ures r ve.

~UJ 1000

10-' Failures per Event~N,~

f

500

--

_

"

I

~ - /-

/

,// /

~

/

/

/

. / / /

~"~ /

~"~ ~. / ~

"

/ ~

---

~-__Code .... Limit Curve 0.23% Cu and 23.0°FIRTNDT EOL Fluence

0

I

1O0

i

i

i

200

I

300

I

400

I

500

TEMPERATURE °F

Fig. 26. Constant failure rate pressure/temperature curves at EOL fluence, compared with the code-allowable limit curve for reactor shutdown.

5. Concluding remarks Recent trends in RPV structural integrity evaluation methodologies have been reviewed, discussing critical aspects related to loading conditions, material properties, crack shape and dimensions and Fracture Mechanics models. For the sake of brevity, not all of these subjects could be deeply discussed and in some cases only general descriptions of models and fundamental results have been reported. Nevertheless it is hoped that the work may be useful as a guidance for deeper analyses of the single topics. As very general conclusions for the reported survey, the following points may be considered. (1) Validation experiments have shown that LEFM can provide sound estimations of RPVs behaviour under severe thermal transient loading; this is of particular importance for old-design vessels which may exhibit pronounced irradiation embrittlement during operating life. (2) Possible improvements to current LEFM analyses may come from a better characterization of upper transitional crack arrest properties, structural cladding effects and residual stress values and significance. (3) EPFM methods have to be included in the evaluation of new-design vessels, in which ductile behaviour is expected throughout the service life; for design applications of these methods extensive material characterization is still needed, coupled

with improvements in experimental techniques for measuring ductile toughness and resistance to crack extension. (4) Fatigue crack growth has a limited relevance to RPV integrity if under-clad (dry) cracks are considered. If the possibility of environmental assisted crack growth is admitted, the integrity assessment is more uncertain and current design assumptions are probably overly conservative. (5) Due to the number of independent variables which may affect the RPV structural integrity, the classical deterministic application of FM models cannot give any quantitative estimation of actual safety margins, for which probabilistic methodologies must be applied. (6) General probabilistic models of vessel failure mechanisms can be obtained by the Monte Carlo simulation technique; at present, mainly due to the lack of sound representations of distributions of independent variables, results from these models must not be regarded as absolute estimations of failure probability but rather as useful means for comparing the impact of different parameters and of possible new developments in design, manufacturing, control and operation procedures. References

[1] J.G. Collier, M.R. Hughes, L.M. Davies, Fracture assessment of a PWR pressure vessel, Nucl. Engrg. Des. 75 (1982) 389-404.

98

E. Vitale / Structural integri(v of RPVs

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