1-s2.0-0029549375900837-main

NUCLEAR ENGINEERING AND DESIGN 35 (1975) 87-153. NORTH-HOLLAND PUBLISHING COMPANY

PRESSURE VESSEL INTEGRITY AND WELD INSPECTION PROCEDURE*

Kenneth A. SOLOMONI", David OKRENT and William E. KASTENBERG

School of Engineering and Applied Science, University of California, Los Angeles, California 90024, USA

Received 10 June 1975

The primary objective of this study is to develop a simple methodology which, when coupled with existing observations on pressure vessel behavior, provides an interrelation between nuclear pressure vessel weld integrity and the parameters of the in-service inspection program, including inspection sample size, frequency and efficiency. The basic input information on rate of generation and development of weld flaws of different sizes and types is drawn primarily from published British and German studies taken almost exclusively from welds of non-nuclear pressure vessels. The input information is varied to reflect differences in weld quality and uncertainty of input data. A modified Markov process is employed and a computer code written to obtain numerical results. If it is assumed that the quality of nuclear reactor welds are the same as the quality of non-nuclear welds (i.e. the data base), then, based on the limitations of the model, the predicted critically sized defect concentration is about 50 x 10 -7 per weld at the end of weld life for welds under both high and low stress if ASME, Section XI, In-Service Inspection Requirements are applied. Based on the British data and the less stringent inspection standards (compared to Section XI) the estimated number of critically sized defects per weld at the end of weld life is 250 10 -7 and 170 x 10 -7 per weld for high and low stressed welds, respectively. If it is assumed that the nuclear reactor pressure vessel welds have superior quality to the non-nuclear welds, then the model predicts an appropriately lower probability of critical defects at the end of weld life. A variety oi" other sensitivity studies are included in the report. Also, a simple methodology to provide an optimal weld inspection program which is consistent with a minimum cost criteria is outlined. It should be noted that the results of this study are based onthe limitations of the simple model that was used and on a variety of corresponding assumptions.

Contents

1. In t roduct ion 87 2. Physical descr ipt ion 88

3. Defect generat ion, development and removal model 98

4. Determinat ion of input parameters 107 5. Results 117

Append ix 137 References 153

1. Introduction

1.1. Objective

The pr imary objective of this study is to develop a simple methodo logy which, when coupled with existing obser-

vations on pressure vessel behavior, provides an interrelat ion between pressure vessel integrity and the parameters of

the in-service inspect ion program, including inspect ion sample size, f requency and efficiency. A modi f ied Markov process is employed and a computer code wr i t ten to obta in numerical results.

* Prepared for the National Science Foundation under Grant GI-39416: 'A General Evaluation Approach to Risk-Benefit for Large Technological Systems and its Application to Nuclear Power'.

1" Present address: NUS Corporation, Sherman Oaks, California 91403, USA.

88 K.A. Solomon et al., Pressure vessel integrity

The basic input information on the rate of development of flaws of different size is drawn primarily from published British and German studies; the input is varied to reflect changes in vessel quality. A simple methodology to provide an optimal weld inspection program which is consistent with a minimum cost criterion can be formulated.

1.2. Basis for approach

All modern pressure vessels, whether they are used in nuclear reactor applications or other applications, are com- posed of welded sections. Experience indicates that under most circumstances when pressure vessel integrity is lost, it is due to loss of weld integrity rather than loss of integrity of the base metal sections. As a result, this study will emphasize the potential loss of pressure vessel integrity due to failure of one of its welds.

A pressure vessel weld fails (or is on the verge of failure) when it contains a defect of critical size for the existing conditions, i.e. the defect can propagate rapidly [1-4] . All welds, no matter how perfectly they are made, initially contain defects [1-7]. Many are small and undetectable, others are large enough to be detected but too small to require repair, and still others may be large enough to require repair. Of those defects that are large enough to require repair, most may be detected and repaired; however, some may not be detected and as a result, not repaired. It has been observed that defects can increase in size over time. The exact development mechanism is not considered in this study which relies on empi.rical observations of defect development. The initial defect size, defect generation rate and defect development rate are approximated from existing information on weld defects.

The pressure vessels used in nuclear reactors are similar in design and characteristics to some of the pressure vessels used in other applications [ 1-10]. Although considerable information exists regarding the integrity of non- nuclear pressure vessels, rather less experience is available for nuclear pressure vessels. As a result, to obtain a basis for approximating nuclear reactor pressure vessel integrity, more expansive data on non-nuclear reactor weld failure has been studied. An attempt has been made to examine data for welds of generally similar type and under similar stress to the nuclear reactor pressure vessel welds.

1.3. Scope of the study

This study begins by describing various types of pressure vessels, pressure vessel welds, weld defects and inspection techniques. A model is formulated to approximate mathematically the process of defect development by assuming that defects are of discrete sizes and develop at discrete rates.

The model consists of a modified Marker process, used to simulate the defect generation and development pro- Cess, and a modified renewal theory technique, used to simulate defect repair. The model input parameters include initial defect size; defect generation rate and development rate as a function of defect size; and defect inspection and repair efficiency as a function of defect size. Input parameters are then selected such that, together with the model, a fit is obtained to available empirical information. The fit is not unique.

2. Physical description

In this section a physical description of a nuclear reactor pressure vessel and its welds is given [ 1-11 ]. Generation and growth of defects in welds and eventual weld failure are discussed [ 12-18]. Also, a description of the inspection procedure and inspection technique is given [ 19-29].

2.1. Pressure vessels and vessel welds

There are various types of pressure vessels in existence which include: (a) boiler steam drums [I, 2] ; (b) liquid pro- pane or other gaseous storage tanks [2, 3] ; (c) fired super heaters [3] ; (d) package boilers [3] ; (e) steam generators [2-6]; and (f) nuclear reactor pressure vessels [4-6]. These pressure vessels are designed to contain pressure between 100 and 32 500 psi [1-6].

K.A. Solomon et at, Pressure vessel integrity 89

2.1.1. Nuclear pressure vessels Many of the earliest nuclear power plants, including the UK gas-cooled systems and the first US gas cooled reactor plant, used ferritic steel pressure containment vessels [6 -11] . The later UK gas-cooled reactors and the French gas-cooled reactors used concrete vessels [6 -11] . However, the fight water reactors are more interesting in view of their larger numbers.

The vessel which serves the important function of containing the highly pressurized reactor coolant water as it flows over the nuclear fuel core is usually made up of four major welded segments [7]. These segments include the top closure head, the nozzle course, the cylinder course and the lowor head [7]. Fig. 1 [1] shows the pieces of a pressurized water reactor (PWR) vessel before its final assembly. A typical 1000 MW(e) PWR vessel has a 14 ft i.d. and is 42 ft high with a cylinder wall thickness of 8~ in. [9]. Boiling water reactors (BWRs) have a similar vessel

J

Fig. 1. Expanded view of PWR vessel showing individual pieces before welding. Cylindrical shell receives highest neutron exposure [ 1 ]

. . . . . . . . ROD CO CHANISMS

ME NTAT ION PORTS HO

Ll! HEAD ASSEMBLY

SLEEVE

UP ROD SHROUD TUBE PL IN1 NN SPRING SU qT PIN

CO ROD GUIDE TUBE 5UPP ROD DRIVE SHAFT

ROD CLUSTER

INLET WN)

UPPE ~IOZZLE CORE

THER~ :~ADIAL SUPPORT

REAC'I

ACCE~

~RE PLATE

RADIAl

CORE )PORT COLUMNS

"NTATION GUIDES

Fig. 2. Schematic view of advanced design pressurized-water reactor vessel and internals [ l ].


[9]. The importance of welding is evident from figs I and 2 [1 ]. A typical BWR or PWR pressure vessel contains about 25 major welds [7]. The volume of each of these welds may vary between 150 and 500 in. 3 [1 -5] .

Several processes could conceivably degrade the material properties during service, including temper, strain aging and irradiation embrittlement. The low alloy SA-533 and SA-508 materials used in nuclear pressure vessels are relatively insensitive to the first two phenomena [7, 9]. Also, they are given a post-fabrication anneal at 1000F which is expected to make them still less susceptible to both temper and strain aging embrittlement at peak operating temperatures below 600F [7, 9]. The integrity of both SA-533 and SA-508 steels may be de- creased by irradiation, particularly at the belt line where the neutron fluence is highest [5-16] .

2.1.2. Nuclear pressure vessel welds Nuclear reactor pressure vessel welds could be grouped into nine categories (see table 1) [5 -16] . Each of these selected groupings have their own defect generation and development potential that are a function of (a) steady state pressure load; (b) external load; (c) cyclic load; (d) seismic load, etc. For ease of model development and sub-

Table 1. Comparison of variables affecting disruptive flaw propagation in stratified weld groups [5-16].

Steady External Cyclic loads Seismic Fabricability Preoperation Flaw Post-operation state loads loads inspectability detection inspectability pressure Pressure Thermal sensitivity load

1. Dome and shell 5 1 2 4 0 3 3 5 1 flanges

2. Cylindrical 5 2 2 2 1 1 1 1 2 shell

3. Bottom dome 5 0 2 2 0 3 1 1 1

4. Bottom dome 5 0 2 2 0 4 4 4 4 penetrations

5. Coolant nozzle 5 3 2 5 3 5 2 2 2 openings

6. Combined 5 5 2 5 5 5 2 2 2 coolant nozzles and supports

7. Support skirt 5 3 2 3 3 4 3 3 4

8. Top dome 5 0 2 2 0 1 1 1 1

9. Head bolts 5 1 2 0 1 1 1 1 1

Rating basis: 0, not applicable; 1, of minor significance; 2-4, intermediate rating grades; and 5, could be controlling effect on flaw propagation.

Notes; (1) Because of inspection technology limitations, flaws in thick flange forgings are less easily detected than in other vessel base

materials. Probability of critical size flaws is thus increased in the initial structure. Flaw growth due to load cycling should be very slow. In-service inspection access is assumed excellent.

(2) Inspection technique should minimize concern for critical size flaws in the shell courses. Welding methods are conventional and the highest quality should be attainable. Heat treatment is the least controllable fabrication variable, but quality control actions should assure effective end results. Final inspection should disclose fabrication and heat treatment defects involving cracking. Cyclic loading effects are infrequent and combined stresses are lower in this .section than in other parts of the vessel. Flaw growth is not expected to be accelerated by the loading conditions. In-service inspection access is good, making flaw detection convenient during post-operation inspection.


sequent presentation, this table was simplified. In particular, it was assumed that there may exist two major groups of welds; those under low steady or cyclic load and those under moderate or high steady or cyclic load. Those welds classified as low stress welds include: (1) welds whose direction of defect development is parallel to the direc- t ion of stress, and (2) defects under low stress. Welds classified as moderate or high stress have a significant compon- ent of moderate or high stress that is perpendicular to the direction of defect development. Those velds under low stress include main course welds. Welds under moderate to high stress include nozzle-to-vessel welds [9, 15].

2.2. Defect generation and propagation in pressure vessel welds

Prior to vessel operation there are defects present in the vessel weld [7, 9]. Most of these defects are very small and do not require repair [9, 10]. During vessel operation these defects may grow and still others may be generated [9, 10]. Defects may be one linear, planar or volumetric dimensional [15].

2. 2. I. Pre.service flaws The pre-service flaws may be in the base metals being fabricated or in the weldments [6 -16] . This study is con- cerned with those flaws found in the weldment and heat-affected zone because experience has shown that these areas are more susceptible to failure than the base metals [5, 6].

In weldments, the pre-service defects that could potential ly be found are entrapped slag, inadequate penetration, incomplete fusion, porosity, and cracks o f various types that can occur either parallel to or normal to the welding directions [6 -16] . Entrapped slags may be small, medium or large and are usually subsurface [7 ,9] . I f they are small, their appearance is similar to porosity [9]. If they are large, they behave in a way similar to lack of fusion or incomplete penetration [9]. Inadequate penetration is similar to incomplete fusion and may be small, medium or large subsurface defects [10, 11]. They may reduce fatigue life and may lead to brittle fracture [10]. Porosity

defects may be small, medium or large [ 11 ] and either subsurface or surface. Subsurface porosity defects are con-

(3) Initial inspection is convenient. Nozzle opening cutout should give good exposure of material interior conditions. Fabrication of nozzle inserts is difficult and could introduce some weld flaws, but inspection techniques for nozzles are highly developed. Cyclic loading in the head is infrequent and combined stresses are low. Flaw propagation rates should be very slow. In-service inspection access to this region is poor, but dome section welds can be examined effectively in more recent head design.

(4) Initial inspection is difficult and nozzle installation is awkward. Weld flaws could exist in nozzle-to-ligament welds. Cyclic loads are small but high peak stresses in nozzle attachments are relieved by shakedown. No significant flaw growth is expected. In- service inspection is very awkward for ligaments. The weld cross section is small and the welds probably would not contain flaws of a size that would cause concern for their growth.

(5) Initial inspection access is assumed excellent but heavy nozzle forgings are more prone to flaws than plate. Fabrication methods for installation nozzle forgings in shell openings are difficult and defects have b~en experienced that were not exposed by radiography but were found by ultrasonic examination. Combined loads on this zone are the highest in the vessel and include very high stress concentration at the nozzle-to-sheU junction, thermal cycling pump reactions due to thermal expansion and seismic forces on the pipe. The high combined stresses make this region the most likely candidate for flaw growth. In-service inspection access to this area is good, so flaw growth can be exposed,

(6) The same commentary concerning coolant nozzle openings applies here, but loadings are increased due to vessel weight which is carried by these nozzles.

(7) Initial inspection access is fair. The skirts are fabricated by weld build-up to provide an attachment for the skirt ring. The quality of the attachment is sensitive to fabrication control. Cyclic loading is infrequent but combined stresses could be severe if pressure, seismic and thermal loadings have to be considered simultaneously. In-service inspection access in this region is poor. Because of infrequent cycling, flaw growth rate should be slow and flaw growth is probably not important if the initial quality control rigorously eliminates fabrication flaws.

(8) Inspection access is excellent, fabrication methods are convenient when few penetrations are used. Load cycling is infrequent. The main cyclic effects occur during start-up and shutdown for refueling. In-service inspection access is excellent and, if necessary, the top dome is replaceable. This is the least likely region for catastrophic flaw growth.

(9) Initial inspection is excellent. Bolts must be preloaded to oppose thermal expansion and the loadings control methods are crude. Redundancy insures against propagation of single failure. In-service inspection frequency makes common mode failures that destroy structural integrity extremely unlikely.


Table 2. Effect of weld defects on properties [7, 9, 16].

Defect Size Location Working temp. range

Effect on cited property

Overfill large surface to small

Undercut small surface

Lack of fusion large subsurface to small

Arc strikes small surface

Haz cracks large surface or longitudinal to small subsurface or transverse

Hydrogen small near cracks in surface stainless cladding

Crater pipes usually subsurface small or surface

Porosity large subsurface to small

surface

Slag large usually inclusions to small subsurface

Hardened large surface or areas in to small subsurface weld

brittle

tensile-improces fatigue-notch effect of overfill may decrease life

may significantly reduce fatigue life particularly in higher strength steels

reduces fatigue life; may lead to brittle fracture

crack initiator reducing fatigue life; may also lead to failure in brittle range

must be repaired, critical in brittle or semi-ductile range; repeated weld repairs often initiate cracks

relatively harmless; if the cracks propagate, it is usually parallel to surface; similar to lack of fusion between clad and base metal

fatigue crack initiator; should be repaired; also brittle fracture starter

considered least dangerous weld defect; little or no effect on tensile fatigue; impact properties

may grow together under cyclic loads and develop crack; should be removed at surface

if small, similar to porosity; larger, longer inclusions may behave like lack of fusion or incomplete penetration

may increase corrosion resistance; will induce KIC and could lead to brittle failure since cracking often accompanies hardening

sidered the least dangerous [10]. They have little or no effect on tensile, fatigue and impact properties and are not expected to grow [10]. The surface porosity defects may grow together under cyclic loads and develop cracks [15, 16]. Longitudinal and transverse cracks are considered to be the most dangerous [9-16] and may be small, medium or large and may be subsurface or surface [16]. Each of the defect types discussed above may have their own particular initial concentration [5]. A summary of the defects that could potentially be found in weldments is given in table 2.

The quality of the base metal and the weld determine to a large extent the probability of flaws being initially present [9, 15]. The initial ~ondition of such vessel welds is established mainly by the applicable construction code.

The flaws which are likely to be present in a fabricated vessel prior to service are of two general categories: those which are within the acceptance standards of the code under which the vessel is constructed and those larger ones which escape detection by non-destructive testing techniques, either because of the limitations of the inspection process, the limitations inherent in the material being inspected, failure to apply the inspection process at the proper stage of manufacturing, or simply misapplication of the procedure on the part of the fabricator. I t is generally con- cluded that defect sizes which are within the acceptance standards of the codes and specifications are based on very

K.A. Solomon et ai., Pressure vessel integrity 93

conservative estimates of their influence on vessel failure [ 19, 20]. There is a continuing research and development effort throughout the world to improve the detection and discrimination characteristics of non-destruCtive testing techniques [19, 20].

2.2.2. In-service flaw generation and development Structural failure usually involves the generation and the slow development of a crack to a critical size at which time failure occurs by rapid crack propagation if the vessel remains in operation [7, 9]. Almost invariably, such crack development is the extension of either a crack which initiates in a highly stressed region or a crack-like defect which remains after fabrication [9-12]. In the former case, the crack may initiate due to either a high constant stress or a cyclical stress with a high mean value [7]. In the latter case, the defect may have been too small to be detected during examination or may have been overlooked due to errors in examination [9]. In either case, high stresses are required for subsequent crack extension at temperatures for which the material is ductile unless a cluster of smaller defects join together [10]. In considering the.types of vessel structural failures possible tn testing or in service, it is convenient to divide the flaw development process into two stages: (1) slow crack development under cyclic or constant load and (2) final failure by rapid crack propagation.

2.2. 2.1. Slow crack growth. This may occur by fatigue or corrosion fatigue, by hydrogen cracking or by stress corrosion cracking. Fatigue and corrosion fatigue damage and crack growth in welds may be caused by cyclic stresses from pressure, mechanical or thermal loading including transients [6]. Defects which are too small to be detected by ASME Code examination procedures are not likely to propagate to disruptive failure under conditions encoun- tered in normal reactor vessel service [6, 9]. Larger defects, undetected through error or poor inspection procedure, might grow sufficiently to cause either leakage or rapid fracture [ 10]. The development rate is frequently stated to be directly proportional to both the defect size and the amount of stress normal to the direction of development of the defect [9, 10].

Low yield strength nuclear vessel welds are generally not highly susceptible to hydrogen-induced crack formation [9]. However, Kussmaul and co-workers in the Federal Republic of Germany (FRG) have reported cases of hydrogen cracking in the heat-affected zones of welds of 21 NiMoCr 37 steel [12-14, 18].

It is well recognized, both in the FRG and the US that some combination of severe constraint, insufficiently dried electrodes or other welding materials, insufficient time and duration of preheat or postheat, etc. may lead to hydrogen cracking [9, 12, 18]. Correct welding techniques will minimize the risk of cracking. Proper inspection techniques should detect significant cracks prior to placing the vessel in service, but small or incipient cracks might not be detected [4, 5]. It is conceivable that even a large crack may remain undetected.

In the FRG, an extensive investigation is proposed to explore the effects of all the important parameters on hydrogen cracking and embrittlement of 21 NiMoCr 37 [12, 13]. No such cracks were reported in the US as at the beginning of 1974 [12, 13].

In a weld initially free from hydrogen-induced defects, there appears to be no mechanism by which large amounts of hydrogen could enter and be retained in the weld and cause subsequent embrittlement or crack formation in service [9, 12, 15]. Corrosion, stress corrosion, localized pitting and crevice corrosion could occur in welds exposed by localized cladding failure [9, 10], but these are not expected to lead to cracking [9] and the rate of chemical attack is expected to be so slow that large flaws should not develop [9, 13].

2.2.2.2. Rapid crack propagation. This is assumed to occur in welds by two processes, i.e. cleavage or ductile tear- ing rupture [7, 9]. Cleavage is the predominant mode of fracture at temperatures below the nil ductility transition (NDT) [7, 9]. At higher temperatures, increasing microscopic ductility causes the fracture mode to change to the ductile tear model [9].

In the transition temperature region, from NDT to approximately NDT + 200 F, fracture occurs by a mixture of cleavage and ductile tear [7, 8].


2.2.3. Summary Prior to reactor service some weld defects exist. After inspection most of the larger defects are removed. After the reactor becomes operational, several influencing factors may cause the defects to develop. The rate of development is usually assumed proportional to the amount of stress normal to the direction of development of the defect, the frequency of cycling and the size of the defect. The defect (if under stress) will continue to develop to criticality unless it is detected and repaired. Critical defects have been observed although the detailed development process leading to this has not been identified.

The initial size of the defect, its rate of development and its ultimate size at failure are functions of several parameters including: (a) the particular weld type; (b) the amount of stress on the weld; (c) the frequency and intensity of the stressing cycles on the weld; (d) the defect type; and (e) the weld and base metal material. It would be very difficult to develop a theory of defect propagation based on all of these parameters since it may not be possible to estimate, quantitatively, their influence on crack propagation. Rather, it may be advantageous to develop a theory based on existing data of actual defect size and growth rate. Owing to a limited history of nuclear pressure vessel welds, a major portion of the empirical data is extrapolated from a history of several million welds and weld years on all types of pressure vessel welds that appear applicable [6-16].

The significance of weld defects anticipated in nuclear systems is a function of several factors [7, 9, 12, 15, 16] : the size, shape, orientation and location of the defect; the type of stresses at the defect location; strength and notch sensitivity of the weld metal; strength and notch sensitivity of the base metal compared to the weld metal; working temperature; and working environment. Therefore, it is difficult to select a quantitative value for the size of a typical critical defect.

2.3. Weld inspection techniques and procedures

The weld inspection technique and procedure will now be described briefly for non-nuclear and in detail for nuclear vessel welds. The purpose of studying the inspection procedure and techniques for non-nuclear pressure vessel welds is to extrapolate the expected defect concentration at a given time from the number of defects actually found, the inspection efficiency, and the percentage of the weld inspected. Once the length of the inspection interval is known, the defect development rate can also be approximated. The nuclear vessel weld inspection techniques and procedures are examined in order to apply the extrapolated data to nuclear systems.

2.3.1. Inspection techniques and procedures for non-nuclear welds Most non-nuclear pressure vessel weld defect data comes from information obtained from the British [6, 8, 10, 11 ] and the German [ 12-14, 18] literature, although some data is available from the US [7, 9, 26].

The inspection of Class I pressure vessel welds in the UK varies from code to code but in general employ the following pattern [6, 8, 10, 11,20] : (1) during construction 50-100% of all pressure vessel welds are examined by radiographic techniques; (2) ultrasonic examination of up to 100% of all welds prior to vessel operation is not generally required except for nuclear pressure vessel welds; (3) visual examination at all stages of construction; (4) pressure testing prior to vessel operation; and (5) radiography (or recently, ultrasonics as an alternative) of main welded seams only (this may be 100% of weld or on a sample basis).

Although these codes are suggested, compliance is not compulsory in the UK .[6, 8], and it has therefore been assumed (in an attempt to be conservative) that only 50% of the welds are initially inspected. The data was collec- ted from 1 July, 1962 to 30 June, 1967.

The choice of techniques'applied in Germany depend upon: (1) the pressure vessel type and operating conditions; (2) the properties of the vessel and its internal and external structure; (3) the kind and size of flaws and cracks and the kind of other material deteriorations to be detected; and (4) the effectiveness of test materials. The Germans have two categories of techniques: integral and local [ 19]. Integral methods determine any serious changes in the weld while local methods are confined to specific portions of a weld. Integral techniques include the overpressurizing test, tests with surveillance specimens, leak tests, and acoustic emission tests. Local techniques include

K.A. Solomon et al., Pressure vessel integrity 95

visual, optical, replica, dye penetrant, magnetic particle, eddy current, infra-red (i.e. thermal emission), conduc- tivity, ultrasonic, and transmission techniques.

In Germany it is recommended that 80-100% of the welds be inspected prior to vessel operation [21, 22] and it is required that all 'accessible' welds be inspected yearly [21,22]. Every four years the vessel should be dismantled and all welds completely inspected; every eight years overpressurizing tests are required. Equivalent procedures and techniques may replace one another, the overpressurizing test, particularly, may be replaced by non-destructive methods. Detailed inspection techniques have been published [21,23, 24].

Based on the number of defects found in welds applicable to nuclear vessel welds, the inspection efficiency, inspection technique and length of the inspection interval; the defect concentration, generation rate and development rate can be calculated. These parameters could then be applied to nuclear systems.

2. 3.2. Inspection procedures for US nuclear reactor pressure vessel welds Section XI of the ASME Boiler and Pressure Vessel Code discl~sses the pre-service and in-service inspection of nuclear reactor pressure vessels and pressure vessel welds [28]. In general, the inspection procedure can be described as follows. During some initial time interval, 0 ~< t ~< 8o (i.e. the zeroth inspection interval) either all or a portion of the welds are inspected with an efficiency of 100% or less. During the next time interval, 8~ < t ~< 8 o (i.e. the zeroth repair interval) all defects of significant size that were detected during 0 ~< t ~< 8 ~ are repaired. It has been assumed that once a sizeable defect has been detected, there is essentially a 100% probability that it will be reduced in size so that either it does not merit repair or is too small to be detected. The probability of not being able to repair a weld defect or replace a weld, given that it is known that the defect is present, is insignificant [9], assuming proper access for welding. Of course, it is possible that a vessel will continue to be operated with known defects.

During the time interval 80 ~< t ~< T1 (i.e. the first development and generation cycle) pre-existing defects develop and new defects are generated. During the first inspection interval, TI ~< t ~< T1 + 8'1, a portion of the welds are inspected with an efficiency of 100% or less. During the first repair interval, TI + 8'1 < t ~< T1 + 8 l, essentially all of the defects that were located during T1 ~< t ~< T1 + 8'1 that required repair are repaired. This process is continued and is shown in fig. 3.

In general, the length of the development and generation cycle is several orders of magnitude longer than the length of the inspection and repair intervals (i.e. Ti >> 8i + ~, Vi).

The current US nuclear reactor pressure vessel weld inspection procedures are described in detail in the ASME Boiler and Pressure Vessel Code, Section XI [28]. A summary of the standards is given here.

Nine stratified nuclear reactor pressure vessel weld types have been identified in table 1. Toreduce modeling complexity, only two types of weld will be considered: those under low steady and cyclic stress and those under moderate and high cyclic stress.

During the time interval 0 ~< t ~< 8~ (i.e. the zeroth inspection) 100% of both the high and low stress welds are assumed to be examined using at least one surface technique (e.g. dye penetrant) and at least one volume technique (e.g. ultrasonic).

It is intended that the in-service examinations be performed during normal plant outages such as refueling or maintenance shutdowns [28]. The inspections are specified in terms of what is required during three successive generation and development cycles. At least 25% of the examination required during three successive generation and development cycles shall be completed by the expiration of the first generation and development cycle (with credit for no more than 33~% if additional examinations are completed) and at least 50% shall have been completed by the expiration of the first two generation and development cycles (with credit for no more than 66~%). The remaining required examination shall be completed by the end of the third generation and development cycle [281.

Where the extent of inspections require the examination of all welds during the first, second and third inspection intervals (i.e. for high stress welds) the same portion of the weld inspected by the first inspection interval will be inspected again during the fourth inspection interval. This rotational basis shall be used throughout the success-

96 K.A. Solomon et aL, Pressure vessel integrity

TWELFTH DEVELOPMENT AND GENERATION CYCLE

ELEVENTH REPAIR INTERVAL ELEVENTH INSPECTION INTERVAL

12 I ~ T i

i=1

11 / i=~1 Ti+611

11 i =~1 Ti+ ~11

T SECOND DEVELOPMENT AND |

J GENERATION CYCLE

FIRST REPAIR INTERVAL { FIRST INSPECTION INTERVAL

FIRST DEVELOPMENT AND GENERATION CYCLE

I ZEROTH REPAIR INTERVAL

ZEROTH INSPECTION INTERVAL

11 T i

i=1

T 1 + T 2

TI + ~1 T1+5 ~ T 1

t 5 o | REACTOR START UP

Fig. 3. Inspection, repair, development and generation.

ire inspection intervals. Where less than all of the welds are required to be inspected during the first, second and third inspection intervals, a similar portion of the weld not previously inspected (other than the pre-operational examinations) shall be required in each successive inspection interval [28].

2.3.2.1. Low steady stress, low cyclic stres~ For pressure-containing welds in the reactor vessel belt line region, at least 3.33% of the length of each longitudinal weld and 1.67% of the length of each circumferential weld are required to be examined during each inspection interval [28]. When the longitudinal and circumferential weld have received an exposure to nehtron fluence in excess of 1019 nvt (energy of 1 MeV or above) the length of weld in the high fluence region to be examined shall be increased to, at least, 50% [28].

For pressure-containing welds in the vessel shell and meridianal and circumferential welds in vessel heads, the the area to be examined includes weld and base metal for one plate thickness beyond the edge of the weld [28]. The examinations performed during each inspection interval shall cover at least 10% of the length of each longitudinal shell and meridianal head weld, and 5% of the length of each circumferential shell and head weld [28].

K.A. Solomon et aL, Pressure vessel integrity 97

2.3.2.2. Moderate steady stress, moderate cyclic stress. For pressure-containing welds in the vessel penetration, the areas subject to examination shall include those pressure-containing welds of reactor control rod penetration in reactor vessel heads, in the control rod drive housings, at vessel instrumentation connections and at heater connections in pressurizer vessels, among which a weld failure in any single penetration results in conditions that fail to meet the exclusion criteria. The examinations performed during each inspection interval shall cumulatively cover at least 8~% of the vessel penetrations [28].

2.3.2.3. High steady stress, high cyclic stress. For nozzle welds, vessel-to-flange welds, and dissimilar metal welds, the individual examinations performed during each inspection shall cumulatively cover 33~% of each weld [28].

2. 3. 3. Inspection techniques for US nuclear reactor pressure vessel welds Inspection categories (i.e. inspection types), for the pre-service and in-service inspections are visual, surface and volumetric [28]. Each term describes a category of techniques, permitting a selection of different techniques for each specified method to accommodate varying degrees of accessibility and radiation levels.

A visual examination is employed to report on the general condition of the weld to be examined, including such conditions as scratches, wear, cracks, corrosion, erosion or other linear or planar defects on the surface of the welds [ 15, 17, 18]. Direct visual examination may be performed when access is sufficient to place the eye within 24 in. of the surface to be examined and no less than 30 with respect to the surface to be examined. Remote visual examination may be substituted for direct visual examination to permit the inspector to satisfy himself that no adverse conditions exist. Remote visual examinations may include visual aids such as telescopes, periscopes, boroscopes or fiber optics [24].

Surface replication methods shall be considered acceptable provided the surface resolution is at least equivalent to that obtainable by visual observation [9]. 3, surface examination is specified to delineate or verify the presence of surface or near-surface cracks, discontinuities or other types of linear or planar surface defects, and may be con- ducted by applying either a magnetic particle examination or a liquid penetrant examination where the surface condition, material and accessibility permit such an examination [ 15, 17].

Magnetic particle examination provides a method for the detection of rounded discontinuities, cracks and other linear discontinuities in welds [ 15, 17]. Magnetic particle inspection is performed by the application of a magnetic field to the inspection area. This field can be created by direct current prods in which the current passes through the weld, or by an alternating current yoke arrangement which introduces a magnetic field in surface layers. In either case, a defect residing in the field will interrupt the magnetic lines of force. Such perturbations in the field will attract magnetic particles dusted on the surface. Sensitivity is greatest for surface defects and diminishes rapidly with depth below the surface. The two processes have certain inherent characteristics. The d.c. inspection process is capable of detecting defects at a maximum of ~ in. belo~v the surface, whereas the a.c. process is limited to defects which are essentially on the surface. In both cases linear indications as short as 1~ in. can be detected, providing that the defect is properly oriented to the magnetic field [24].

The liquid penetrant examination provides a method of non-destructive examination for the detection of discontinuities open to the surface of the weld. Typical discontinuities detectable by this method are cracks, seam laps, cold shuts and laminations. A liquid penetrant is applied to the surface to be examined and allowed to enter such openings, the excess penetrant is removed, the part dried and a developer applied. The developer is wetted or stained by the penetrant entrapped in the discontinuity and increases the evidence of the discontinuities so that they may be seen either by ordinary light or by the use of a black light [24]. This technique is used extensively in pre-operational inspections for ensuring the integrity of the weld; however, because of its nature, the application to in-service inspection is somewhat limited. The detection limit of flaws by liquid penetrant and magnetic particle techniques depends on the process, the penetrant materials employed, the operator, the viewing conditions em-


ployed, the surface finish, and to some extent, the nature of the defects. It is not unusual to detect a defect which is as shallow as 0.001 in. [ 15, 17]. Cases have been reported of missing weld defects several inches long and 0.25 in. deep [15, 18].

A volumetric examination is used to indicate the presence of subsurface discontinuities with a method or technique capable of examining the entire volume of the weld contained beneath the surface. One-, two- and three- dimensional defects can be detected. Methods, such as radiographic ultrasonic examination, or other newly developed techniques, may be employed provided the method is demonstrated to be capable of detecting subsurface discontinuities [15, 17, 18, 24].

Radiographic techniques, employing energy sources such as X-rays, gamma rays or thermalized neutrons, may be utilized with appropriate image-recording techniques such as photographic film or papers, electrostatic systems, direct image orthicons or image converters [24]. The use of radiographic examination for in-service inspections has generally not been fully explored for reactor pressure vessel welds because the radiation environment is high enough to cause film fogging [ 17]. Radiographic inspection is limited in detection capability with regard to cracks; fatigue cracks especially tend to be located in areas of cross-sectional changes which are difficult to radiograph [17].

The most popular method considered for in-service inspection is ultrasonic testing [ 15, 17, 18, 24]. Its different principle (reflection from a discontinuous surface) from that of X-rays, plus its capability for application in a multi- plicity of directions, makes it a powerful technique.

3. Defect generation, development and removal model

In section 2, the assumed physical process of weld defect generation, development and removal is described. In a nuclear reactor pressure vessel weld, some defects may exist prior to the zeroth inspection (i.e. prior to vessel operation). During the zeroth inspection and repair processes the larger, more dangerous defects are removed. During the first generation and development cycle the existing defects develop and some new defects generate. Some of the defects that are found at the first inspection interval are repaired. The above process continues through several inspection intervals, repair intervals, and generation and development cycles. During any inspection, only a portion of the welds may be inspected with a less-than-perfect efficiency.

In this section a purely mathematical model is developed to approximate the assumed physical process of defect generation, development and removal.

3.1. Model assumptions

The model assumes that the weld defects may initially be of five distinct sizes rather than using a continuous distri- bution of sizes. These five discrete sizes have been assumed because (1) the quality of the available data on defect sizes is not fine enough to distinguish between a continuous spectrum of sizes or more than five discrete sizes and (2) the mathematical model used to treat the physical process is considerably more simple for the discrete defect size.

The quantitative values of the inspection and repair efficiencies are approximated if sufficient data is available, or otherwise assumed. The assumed data is not completely arbitrary since it is known that the inspection and repair efficiencies are a function of inspection and repair technique, defect size and the number of prior inspections and repairs at the defect site. The quantitative values of generation and development rates are approximated from existing data.

This model uses empirical information to approximate the expected concentration of defects at a particular time rather than using a 'first principal approach' or a 'mechanistic approach'.

K.A. Solomon et aL, Pressure vessel integrity

Table 3. Definition of parameters used in model.

99

Parameter Definition

0

A

C

D

61

a7 Ti

Wi

up(. HB(j)

riP(;) H~-'(]3 tt iB"+ A (/)

l~i ~o ( j )

/~/--,A(j) Px(t)

Qi

kA, i

kB,i

kC,l

Extremely small defects. Defects of 0 size may exist but are either too small to detect or have a less than 50% probability of being detected even with the most sensitive equipment. Even though these defects do not currently present a significant problem, they have the potential to generate to defects of the next larger size (size A). The concentration (or probability) of this defect size does not specifically enter the calculation.

Defects of size A have a minimum probability of 50% of being detected using the most sensitive equipment but are too small to merit repair. Defects of size A have the potential of developing to defects of size B at a rate of

?~A.

Size B defects are larger than size A defects. If defects of size B are detected during an inspection they are expected to be repaired (to defects of size A or size 0). If defects of size B are not detected and repaired, they have the potential of developing to the next largest size defect (i.e. size C).

C is the largest flaw size below 'critical' size. If size C defects are not corrected during the inspection-repair process, they will develop to size D defects.

These defects are of critical size and unlike defects of sizes 0, A, B or C are assumed to develop very rapidly. It is assumed that defects of size D constitute a 'failed weld condition" and vessel failure is unavoidable if operation continues for any appreciable time. Weld defects of critical size are not removed (and placed in smaUer defect size groups) by repair.

The length of the tth inspection interval measured in hours.

The length of the ith repair interval measured in hours.

The length of the ith generation and development cycle measured in hours.

The portion of the weld inspected during the ith inspection measured in percent.

The probability of detecting a defect of size A during the ith inspection using the/th inspection technique.

The probability of detecting a defect of size B during the ith inspection using the/th inspection technique.

The probability of detecting a defect of size C during the ith inspection using the/th inspection technique.

The probability of detecting a defect of size D during the/th inspection using the jth inspection technique.

The probability of detecting a defect of size B and repairing it to a defect of size 0.

The probability of detecting a defect of size B and repairing it to a defect of size A.

The probability of detecting a defect of size C and repairing it to a defect of size 0.

The probability of detecting a defect of size C and repairing it to a defect of size A.

The expected concentration of defects assumed present of size X (where X can be size A, B, C or D) at time t. Px(t) is measured in defects per weld.

The constant number of size A defects per weld hour that is assumed to be generated during the ith generation and development cycle. Qi is called the defect generation rate. Qi is assumed to be independent of the number of defects present.

The rate of development of defects (during the ith generation and development cycle) of distinct size A to defects of distinct size B. The development rate of each size A flaw to size B is constant and is measured in units of inverse hours.

The rate of development of defects (during the ith generation and development cycle) of distinct size B to defects of distinct size C. The development rate is constant and is measured in units of inverse hours.

The rate of development of defects (during the ith generation and development cycle) of distinct size C to defects of distinct size D. The development rate is constant and is measured in units of inverse hours.

100 K.A. Solomon et a, Pressure vessel integrity

3. 2. Mathematical development of the model

Table 3 defines the parameters used in the model. The smallest sized defects are classified size '0' and are defined to be too small to detect or have less than a 50% probability of being detected even with the most sensitive equipment. These defects are assumed to have the potential to generate to defects of the next larger size (i.e. defects of size 'A') at a constant generation rate of Qi defects per weld hour during the ith generation and development cycle (see fig. 3 for a definition of generation, development and repair cycles) which is independent of the concentration of size '0' defects, hence this concentration does not enter into the analysis.

Size A defects are assumed to have a minimum probability of 50% of being detected using the most sensitive equipment but are classified too small to merit immediate repair. They have the potential of developing to defects of size B at a rate of XA, i during the ith generation and development cycle.

Size 'B' and size 'C' defects are classified arbitrarily to be defects that are large enough to merit repair if detected but small enough to be considered a non-critical defect.

Size B defects are larger than size A defects. If size B defects are detected during an inspection, they are expected to be repaired to defects of either size A or size 0. If size B defects are not detected and repaired, they have the potential of developing to the next larger size defect (i.e. size C defects) at a development rate of XB,i during the ith generation and development cycle. Size C defects are potentially critical and if they are not corrected during the inspection and repair intervals, they will develop to size D defects at a rate kc,i. Size D defects are critical and unlike defects of size 0, A, B, or C, are assumed to develop at a very rapid rate. It is assumed that a size D defect will constitute a weld failure if operation continues.

The five discrete sizes, 0, A, B, C and D are selected for convenience. Admittedly, it may be very difficult to distinguish between size B and C defects since both include defects that are large enough to merit repair but yet small enough to be considered an unfailed weld. Two discrete sizes in this repairable range were selected to reflect the fact that a rather wide range of repairable size defects exist. Since the parameters that determine what consti- tutes a repairable defect include defect type, weld type and defect orientation relative to stress, it would be im- practicable to assign absolute sizes to each range. The categories are selected qualitatively based on the defect description.

Figure 4 displays the inspection, repair, generation and development of defects in the model. During the time interval 0 < T< 6o the zeroth inspection takes place where Wo% of the weld is inspected. Size A defects are detected with an efficiency of HoA(/')% using the ]th inspection technique during the 0th inspection; size B defects are detected with an efficiency of Hoa(/')% using the/'th inspection technique; size C defects are detected with an efficiency of HoCU)% using the ]th inspection technique; and size D defects are detected with an efficiency of

If more than one inspection technique is used to detect a size X defect at the zeroth inspection, then the combined efficiency is

HX(l~) = 1 - [ i ='fi {1 - H~(j)}]. (1)

If the efficiency of detecting a size X defect is a linear function of the distance z from the surface of the weld, and if the linear attenuation factor is assumed to be oJ then

HoX(j, z) = HoX(j)e - oz (2)

If the defect'is detected and repair is required, it is assumed that the probability of repairing the defect is about 100%. In other words, the probability of repairing the weld defect (to size 0 or size A) is equal to the probability that a weld of acceptable quality will initially be manufactured (/> 99.9%). IfHX+V(l~) is the net probability of repairing a defect of size X to size Y during the 0th repair interval, then

HoB(X) m HoB~A(x) + HoB~(X), HCo(~,) ~ HoCOA(z) + HoC~(Z). (3)

K.A. Solomon et aL, Pressure vessel integrity

TIME PHYSICAL PROCESS

0~t6 o

Go

102 K.A. Solomon et at, Pressure vessel integrity

At t = 6 o (immediately following the zeroth repair) the expected concentration of defects of sizes A, B, C and D assumed present are Ph(8o), PB(6O), Pc(~o) and PD(~O), respectively. (In subsection 4.1 these expected values are calculated from the actual number of defects found during 0 < t < 6~, the percentage of the weld inspected and the inspection and repair efficiencies.)

From 6o < t < T1 (during the first generation and development cycle) the rate of change in the expected concentration of size A defects is equal to the generation rate per weld hour of size A defects minus the rate of change in concentration of defects that grow out of size A; the rate of change in the expected concentration of defects of size B is equal to the rate of change in the concentration of defects that develop into size B from A minus the rate of change in the concentration that develop out of size B to C; the rate of change in the concentration of defects of size C is equal to the rate of change in the concentration of defects that develop into size C from B minus the rate of change in the concentration of defects that develop out of size C to D; and the expected concentration of defects of size D defects is equal to the concentration of defects that develop out of size C to D. Mathematically, during the first cycle:

dPA(t)/dt = Q1 - XA,IPA(t), dPB(t)/dt = XA,1PA(t) -- XB, IPB(t), (4, 5) dPc(t)/dt- XBAPB(t)-- hc,lPc(t) and dPD(t)/dt = hc,lPc(t). (6, 7)

Subscript 1 on the generation and develop .ment rates corresponds to the first generation and development cycle. The solutions to the simultaneous equations (4)-(7) during the first generation and development cycle are,

respectively,

PA(6O < t


(1/XB,1) {1 - exp(--;kB) l t)) +Pc(tSo) {1 - exp(--Xc,lt)} + ?,8,1Xc,IPB(8O) [ ('\C,I ~'B, 1)

+ (1/hC,l) (1 - exp(-Xc, l t ))] +eD(t - 60). (11) (XB,~ - XC,~) J

At t = T1 + 81 (immediately after the first inspection and repair interval) the expected number of defects per weld of size A is equal to the number of defects per weld that were added to A from repair of defects of size B and size C. The expected number of defects per weld of size B at t = TI + 81 is equal to the number of defects per weld of size B at t = TI minus those that were removed from size B and repaired to size A or size D defects. The expected number of defects per weld of size C at t = Tl + 81 is equal to the number of defects per weld at t = TI minus those that were removed from size C and repaired to size A or size D defects. The expected number of defects per weld of size D at t = TI + 51 is approximately equal to the number of size D defects per weld at t = T1 since repair of size D defects is not assumed to be allowed. Mathematically,

PA(t = TI + 81) =PA(t = T1) +H~-~A(y,)W1PB(t = T1) +HC-'A(y,)WIPc(t = T1) ~--PA(t -- T1) (12, 13)

because

HB-*A(E)WIPB(t = TI ) + HC-*A(E)WIP(t = T1 ) ~ eA(t = TI ), (14)

PB(t = T1 + 61) = PB(t = TI) - (H1B~A(x) + HB-*(Z))WIPB(t = T1), (15)

Pc(t = TI + 61) =Pc( t = Zl) -- (H1C--~A(~) + HCI -~(~) )WlPc( t = Tl), (16)

and

PD(t = TI + ~1) =PD(t = Tt). (17)

During T1 + 81 ~ t ~ T 1 + T 2 (the second generation and development cycle) the expected number of defects per weld can easily be calculated since P A (t = T + 61 ), PB( t = TI + 81 ), Pc( t = T1 + 61) and PD(t = T1 + 61 ) were calculated in eqs (13)-(16), respectively, and the generation and development of eqs (8)-(11) may be adjusted to reflect new initial conditions at t = T1 + 61. Mathematically,

PA(T, +6,


~3

f !

I

I "~ ~ ~ ~I

IH

%/ 4-

.{. II II

J

d;

i '~ ,~~,

+

e~

I 11

f

I

+

I

+

eg

.<

+

i E

+

1

e~

irl

K.A . So lomon et al . , P ressure vesse l in tegr i ty 105

< ,<

I

e~

!

r

,<

+

L

e~

e~

+

t t

I

i ?

~ r ~7

I

e<

I

e~

~J

~i ~.

-I? +

eD

t I

I

f~

,<

ill

sY

? I

I I

I .

,<

,<

,<

J I

t ~" '~ l

,< ,<

i

+

I

106 K.A. Solomon et al, Pressure vessel integrity

+0

exP{-&3,2(t - Tl )I exP l-k,20 - Tl)I

A,2 - hB,2&2 - hB,2) + @A,2 - k,2)(hB,2 - k,2) I

+PC(t=Tl +~,)exP{-k,20- TIN

+ hB,ZPB(t = T1 + 6 1) exP 6hB,P (t - Tl)} + exP {-kc,2 ct - Tl))

&,2 - XB,2) @C,2 - hB,2) 1 (20)

and

PD(T, +61 GtGT1 +T2)=h~,2h~,2&,2e2 t- (1/&,2)[1 - exP{--hA,f@- T,Nl

hA,Z@B,Z - AA,Z)@C,Z - hA,2)

+ t - (lhB,2)[1 - exP{-hS,2(t - T,Nl + f - (1/k,d[l - exp{-&(t - T,))] hB,2@A,2 - hB,2)&,2 - hB,2) k,?@A,Z - k,2)@B,2 - k,2) 1

+ XA,2 hB,2 k,ZPAct = T1 + 6 I ) (l/AA,2)[1 - exP{--hA,2@ - TINI

@C,2 - XA,2)@B,2 - XA,2)

+ (lhB,Z)[l - exP{-hB,2(t- TINI f (l/k,2)[1 - exP{-k,a(t- T,Nl (AA,2 - hB,2&,2 - hB,2) (AA,2 - &,2)0B,2 - AC,21 1

%@=Tl ts,)[l-exP{-~,2(t-T1)}l th~,2k,2P~(t=Tl 61)

(l/hB,2)@ -exP{-hB,2(t- WI1 t(1/k,2)[l -exP{-k,Z(f- T&i tPDtt=T, f61j, &,2 - XB,2) @B,2 - kc,21 I

(W

The second inspection occurs during T, t T2 Q t < T1 T2 6; second repair occurs during T, t T2 t 6; < t < T1 t T2 t t = T1 + T2 + 62 can be calculated from the concentration of defects at 1= T, t T2 and the number of defects repaired during the repair interval.

In general, the expected concentration of defects during the nth generation and development cycle can be calculated from the following matrix equations:

where

(23)

and where the matrices used in eqs (22) and (23) are defined in table 4. To calculate the number of defects present during any generation and development interval the following infor-

mation is required: (a) the initial concentration of defects of size A, B, C and D; (b) the percentage of the weld inspected during the zeroth, first, second, etc. inspections; (c) the inspection efficiency of detecting size A, B, C

D defects rates during the first, second, third, etc. cycles.

3.3. Additional constraints

To recommend an optimal inspection procedure, the economic constraints should be considered. Owing to limited data, the economic constraints will be studied parametrically.

The total cost of inspecting all pressure vessel welds throughout the lifetime of the vessel is the sum of the fixed

K.A. Solomon et al., Pressure vessel integrity

Table 5. Definition of parameters for cost constraints

107

Parameter Definition

CTOT

CF

CV

~(i, J3

X

wi,j

CD i=1,2 . . . . ,n

j=1 ,2 . . . . . m

Total cost of inspecting all pressure vessel welds throughout the lifetime of the vessel.

Total fixed cost of inspecting all pressure vessel welds throughout the lifetime of the vessel.

Total variable cost of inspecting all pressure vessel welds throughout the lifetime of the vessel.

Variable cost of inspecting per ith number inspection, per volume (or surface area) of weld, per/th technique.

Total volume or surface area of weld.

Portion of volume (or surface area) of weld inspected during the ith inspection using the/'th inspection technique.

Total length of time needed during the ith inspection for the/th sequential technique beyond the length of time that the reactor would normally be down for other, unrelated reasons.

Cost per unit of downtime.

The number of inspection intervals during the vessel lifetime.

The number of inspection techniques used during each inspection.

costs and the variable costs. Once the decision to inspect is made. the fixed cost is invariant with respect to the inspection parameters (i.e. the percentage of the weld inspected, efficiency of inspection, length of the inspection intervals, inspection techniques, etc.).

The variable cost associated with the inspection of a weld is a function of the cost of the particular inspection technique, the number of different techniques, the number of inspections, the size of the area or volume of weld insepcted, and the cost per unit of additional downtime required to perform the inspection beyond the time that the reactor would be down for other purposes. The variable cost may also be a function of other parameters that are currently undefined. Based on the above assumptions, the total cost Ca'oa- is equal to the sum of the fixed cost C~ and the variable cost Cv,

Ca'oy --- CF + Cv, where it is assumed that CF = constant, (24)

and tl rr/ rt m

Cv = Y. Z (V~j)(x)(Wi, j )+ Y. ~ (6i, j + 6i, i )Co. (26) i= l /'=1 i=1 j= l

Equation (22) may be combined with eq. (26) to produce five non-linear, simultaneous, first order differential equations (see table 5 for parametric definitions). Using non-linear, dynamic programming an optimal inspection procedure can, in principle, be developed.

4. Determination of input parameters

This section is devoted to determining the input parameters used in the model outlined in section 3. In particular, the following input parameters are required: (1) the expected concentration of defects of a specified size at t = 6o; (2) the percent (or portion) of the welds examined during the zeroth inspection (e.g. W0); during the first inspection (e.g. I4/t); and so on; (3) the inspection efficiency of detecting a defect of a particular size, during the ith inspection, and using the/th type of inspection technique; (4) the repair efficiency of repairing a defect of a particular size back to a defect of smaller size; (5) the absolute defect size for any stratified group of welds and defect types; (6) the generation rate of small defects; (7) the defect development rate; and (8) the length of the inspection intervals. The values of the input parameters discussed above will be extrapolated from several sources of raw data.


Because of the rather limited nuclear pressure vessel experience and the relatively extensive experience in non- nuclear pressure vessels, much of the data has been derived from the latter source. When evaluating the data, considerable care is taken to ensure that all data (non-nuclear and nuclear) is applicable to nuclear vessels. The data represents many vessel years of study in several countries including the US [7, 9], the UK [6, 8, 10, 11], Aus- tralia [6, 15], the FRG [12-14, 18], France [16], Belgium [16, and Austria [16]. Conservative assumptions are made when the data is in doubt.

4.1. Initial number of defects

The purpose of this section is to estimate the expected number of defects of a specified size present in a typical stratified weld immediately following the zeroth inspection and the repair process, but prior to nuclear reactor operation (i.e. time t = 8 o). These input parameters are derived from the following raw data: (1) the number of defects found during 0 ~< t ~ 50; (2) the associated inspection efficiency; (3) the associated repair efficiency; and (4) the percentage of the weld inspected. In subsection 4.3 the range of absolute values of the four distinct sizes of defects (namely, A, B, C and D) are discussed. In general, the classification of defects by size is a function of defect type, defect location and type of weld.

During the zeroth inspection process of N welds, the following number of defects were actually found: FA(60) of size A; FB(50) of size B; Fc(5o) of size C; and FD(5~) ) of size D. The number of defects that could have been found during 0 ~< t ~< 5 0 if the inspection process were 100% complete and 100% efficient, can be estimated once the values of Wo (i.e. the percentage of the weld inspected); HoA(Z) (i.e. the net efficiency of detecting a size A defect during zeroth inspection); HoB(Z) (i.e. the net efficiency of detecting a size B defect); H~o (22) (i.e. the net efficiency of detecting a size C defect); and HD(z) (i.e. the net efficiency of detecting a size D defect) are known. The number of defects that could have been found in the interval 0 ~< t ~< 60 if 100% of the weld were inspected 100% efficiently is for size A, PA(5'o)/Wo(HAo(Z)); for size B, PB(5~) = FB(5'o)/(Wo)(HoB(~)); for size C, Pc(8~) = Fc(50)/(Wo)(HCo(y.)); and for size D, PD(6~) = FD(6'o)/(Wo)(HDo(Z)) = FD(5~). As a result of the zeroth inspection (during 0


The number of defects classified a particular size which were actually found during the zeroth inspection (i.e. 0 < t < 8~) are outlined in table 6 together with the number of defects per weld expected present after the zeroth inspection and repair interval (i.e. t = 80). The rather wide range in the number of defects of a particular classification expected present is due in part to the uncertainty in the magnitude of the model parameters. The significant discrepancy in the range of the number of defects of a particular size expected present using the UK data [10] and the German data [11-14] may be due in part to the assumption that only 50% of the UK welds are inspected during 0 < t ~< ~ whereas 80% are inspected during this interval in Germany. The assumption concerning the number of welds inspected in the UK may be valid and is due to the fact that weld inspection is suggested but not enforced. The assumed 50% inspection area reflects an upper estimate in the actual number of defects of critical size present. The British may, indeed, inspect 100% or nearly 100% of the weld during 0 < t

110

?

x

?

x

x

T

X

d ~ z <

~o

.=.

oo

0

K.A. Solomon et al., Pressure vessel integrity

o%

O~

O~

0

~ O

'4 oO

~0 '4 5c~

! I

~(" l

I I

! I

O0 ?

I I

c~c~ ! I

c~c~

I I

0 0

w~ ~D

I !

06 I

c5

e4

I I

~ 0

I I

oo~.

~O

I f

~ 0 X~'4

I I

~ Q


defects in non-nuclear vessels ":s larger than the concetration of defects in [nuclear vessels for each of the four defect sizes [9, 10, 13]. The limited data on nuclear vessels does not allow us to calculate any quantitative value of defect concentration prior to vessel operation. However, the non-nuclear data provides an upper bound on these concentrations.

4. 2. Percentage o f welds inspected and the corresponding efficiency

In this section the percentage of the weld examined during the zeroth inspection W 0, during the first inspection WI ; during the second inspection W 2 , and so on, will be discussed. The results are summarized in table 7. Foreign weld inspection standards are generally- more relaxed than US standards [19, 20, 27]. Also, standards for inspecting non-nuclear pressure vessel welds are more relaxed than standards for nuclear welds [9, 23, 27, 28].

There are two purposes for estimating the percentage of the weld inspected. First, it is necessary to determine what percentage of the welds are inspected in the past to estimate the expected number of defects that could have been found had all welds been inspected, Secondly, it is necessary to estimate what percentage of the weld is currently being inspected by US vessel standards. This value is taken directly from ASME Il l and XII [27]. For all vessels (foreign and domestic, nuclear and non-nuclear) it is expected that 50% ~< 1t/0 ~< 100% where W 0 = 100% is usually the case [19, 20, 27].

For US nuclear vessel welds under high stress W 1 = I 2 = W 3 . . . . . W12 = 33~% where every fourth inspection examines over the same area (non-overlapping technique). For US nuclear vessel welds under low stress W 1 = I92 . . . . . Wl2 where 2% < W i < 5% depending on weld [27]. It is extremely difficult to estimate the portion of the weld inspected in foreign vessels. A conservative estimate would assume that only 20% of the high stress welds are

Table 7. Percentage of weld inspected (some values are assumed).

Country Wo(%) I i Comment (i = I, 2, 3 ..... 12) (%)

Us(4O,S4) Nuclear

high stress welds I00 331 low stress welds 100 2-5

Non-nuclear high stress welds 100 33 t low stress welds 100 2-5

UK(32,34,3S,44)

All vessels high stress welds (?) 50-100 20-30 low stress welds (?) 50-100 1-5

FR GO6-aa,42,43,46,49) All vessels

high stress welds (?) 50-100 20-30 low stress welds (?) 50-100 1-5

Other vessels 09,40,41 ) All vessels

high stress welds (?) 50-100 20-30 low stress welds (?) 50-100 1-5

according to ASME Code IIl& XI on pressure vessels according to ASME Code Ill & XI on pressure vessels

some degree of uncertainty in valves some degree of uncertainty in valves

rather difficult to estimate W i for i ~ 1 rather difficult to estimate I i for i ~ 1

rather difficult to estimate W i for i ~ 1 rather difficult to estimate W i for i ~ 1

rather difficult to estimate W i for i ;~ 1 rather difficult to estimate W i for i ;~ 1


Table 8. Range of assumed inspection efficiencies as a function of defect classification [8, 10-19, 21, 24 ].

Technique Current standards (1965-1974) Previous standards (prior to 1965) Comments

Stress i= 0 50-70 70-90 90-95 96-99 45-65 70-90 90-95 96-99 volume wave i > 0 50-70 70-90 90-95 96-99 45-65 70-90 90-95 96-99 technique

Pressure i = 0 - - - 99.9 . . . . effective for wave i > 0 - - - 99.9 . . . . large defects

Ultrasonic i = 0 50-70 70-96 90-99.9 98-99.9 50-65 70-96 90-98 98-99.9 volume i> 0 50-70 70-96 90-98 98-99.9 50-70 70-96 90-98 98-99.9 technique

Visual 0-60 60-80 80-85 85-90 0-60 60-80 80-85 85-90 surface exam technique

Dye i = 0 15-60 70-95 90-96 96-98 15-55 70-95 90-95 95-96 surface penetrant i > 0 20-60 70-95 90-96 96-98 20-60 70-95 90-95 95-96 technique

volume Leakage - - - 99.9 - - - 99.9 technique

Radiograph i = 0 0-40 40-70 70-85 98-99 0-30 40-60 70-80 98-95 volume i > 0 10-50 50-80 70-90 98-99 10-40 50-75 70-85 94-98 technique

inspected at each interval and only 1% of the low stress welds [27, 28]. Since the British do not follow a uniform inspection code, it is not known if they use a non-overlapping inspection technique for their high stress welds as is done in the US. As a conservative assumption it has been supposed that the British do not use a non-overlapping technique.

A range of assumed inspection efficiencies per technique for each defect size classification is listed in table 8. The value HX(6) is the efficiency of the ]th technique in detecting (and locating)a size X defect during the ith

inspection attempt.

4. 3. Absolute defect size

The actual or absolute size of the defect (length in inches, area in square inches, or volume in cubic inches) that be- longs to categories 0, A, B, C and D is a function of several parameters. For example, if a defect o f a specific size is under low stress, it may be classified as a type A defect. But, i f that same size defect were subjected to a much higher stress, it would be more likely to develop and would present more of a potential hazard. In that case the defect may be classified as a type B defect. A volume crack may be more of a potential hazard than a surface crack and as a result may belong to a different size classification even though the volume and surface cracks may be of the same absolute length and width. In general, it is very difficult to classify defects according to absolute sizes.

4.4. Generation and development rates

In this section the defect generation rate and the defect development rates will be calculated from existing UK, FRG, and US data [ 19, 21 -23 , 26 -29] . The generation rate during the ith generation and development cycle is


equal to the number of size A defects per weld hour that are generated. The development rates during the ith generation and development cycle are proportional to the number of defects per weld that grow from a defect of a particular size to a defect of the next largest size. The generation and development rates are constant during generation and development cycle, but may change during subsequent cycles.

From the data, the expected concentration of defects of sizes A, B, C and D present immediately following the zeroth repair has been calculated in subsection 4.1 to be PA(60), PB(60), Pc(6o) and PD(6O), respectively. These values were calculated from the number of defects actually found during 0 ~< t ~< 6 o, the number of welds inspected, the inspection efficiency and the percentage of welds inspected. Using the available data, the number of defects actually found during the first inspection (Tt ~< TI + 6~), during the second inspection (Tt + 7"2 ~ t ~< Tt + 6~), and so on, are known. Also, the number of welds inspected, the inspection efficiency, the percentage of welds inspected, and the length of the inspection interval are known during subsequent inspections. As a result, the expected concentration of defects at t = Tt + 6 x, t = Tt + T2 + 62, etc. can be calculated.

The values of Qt, ~.A,l, ~,B,1 and hc, 1 are calculated by solving eqs (8)-(11) simultaneously at t = Tt. The values OfPA(t = 6o),PB(t = 60), Pc(t = bo),PD(t = 6o),eA(t = Tl),eB(t = Tl),Pc(t = Tl) and PD(t = Tt)have been calculated from the existing data (see subsection 4.1). The resulting four transcendental equations are solved for the four unknowns, Qt, XA,1, XB,1 and ?,c,1-

Table 9. Number of defects found during the first five years of vessel service [ 10].

Age Assumed Number (yr) size found Tl classification

Description

5 B 1 3 C 1 5 B 1 5 B 1 3 B 1

small cracks (repair required) in nozzle welds 'high stress welds' cracks 4 in. long x T~ in. deep 'low stress welds' cracks ~ in. long 'low stress welds' small cracks in nozzle welds 'high stress welds' small cracks in plate 'low stress welds'

3 B 1 3 C 1 3 C 1 5 B 1 3 B 1

'low stress welds' 'high stres~ welds' 'high stress welds' 'low stress welds' 'low stress welds'

3 B 1 3 B 1 3 D 1 3 C 1 3 D 1

'low stress welds' 'high stress welds' 'high stress welds' 'high stress welds' ' low stress welds'

3 B 1 3 B 1 3 C 1 3 B 1 3 C 1

'low stress welds' 'high stress welds' 'high stress welds' 'high stress welds' 'high stress welds'

5 B 1 3 A 9 5 A 14 3 A 18 5 A 22

'low stress welds' 'low stress welds' 'low stress welds' 'high stress welds' 'high stress welds'


The values of Q2, ~kA,2, ~kB,2 and hc,2 are calculated by solving eqs (18)--(21) simultaneously at t = TI +/ '2 .

The values OfPA(t = TI + 81) ,PB( t = Tl + 81) ,Pc ( t = T1 + ~I ) ,PD( t = TI + 81) ,PA( t = Tl + T2),PB(t = TI + T2), Pc(t = Tt + 7'2) andPD( t = Tt + T2) are known.

In general, the values o f Qn, hA,n, ~kB,n and hc,n are calculated by solving the matrix equation (22) at t = Y-n= l ti where the values of

i ( ) t= +Sn- I PB t=~Ti+Sn- I PC t=~ T i+Sn- I PD t=~ T i+Sn- I 9 "= i=1 i=1 t= , PB = , t= and PD =

i=1

have been calculated from existing data.

Tables 9 and 10 are a summary o f the number of defects found during 0 < t < 8 ~, and Ti


o

r~

e.. o

b.o

e. o

p.l

Iw. , e...

0

r~

r ,

c:w

I + "".~ o

o I

~:~x

I

o I "~

116 K.A. Solomon et a/., Pressure vessel integrity

"G

0

.o

o

0

=,

IA

v

e-

c~

P .

I

~C x

o I

~C x

(::w

,< x

I

o I


An alternative method of obtaining ~c,i is suggested which consists of modifying a formula on crack growth in other metals [4]. It is assumed that the development of flaws in weld metals and other metals obey the same physical laws. No empirical formula has been derived for the development rate of defects in welds, but a formula does exist for defect development in 7075-76 aluminum [4]. I fN is the number of stressing cycles over a range of +OKst. and a is defect size, then

da/dn = a' {o(rr) l/2a} a[~, _ o0r) 1/2a} ' (31)

where a and/3 are material constants. For simplicity, it is assumed that the specimen experiences a constant rate of cycling so that the rate of growth may be expressed as da/dt.

The length of time taken for one defect of size 0 to grow to size D is equal to

A B C D

f a(a) 3'2 f a(a) 3'2 1" a(a) _ a(a) _ T = j ~ dt + j~_~dt+J~- -~q75c l t+ ~ ~_al/---------~a,. (32) o A B

A lso , B C D

1 f a(a) a/2 _.1__1 = f if(a) a/z 1 f a(a) 3/2 XA, t. =AJ~---~-~ dt, XB, ' ~/3_ al/2 dt and ;kc, 1 = j~_~dt . (33-35)

The value of at. and/3t, can be obtained by solving eqs (33) and (34) simultaneously for each generation and development interval. The value of )~c,t. can then be calculated.

The above methodology is applied to the German and US data and the results are displayed in tables 11 and 12 for low and high stress welds respectively. Note that the values derived are not unique and depend on assumptions made with regard to inspection efficiency, generation rate of new size A defects, etc.

5. Results

The mathematical models developed in section 3 are combined with the data of section 4 to yield a range of estimates on the probability that a nuclear reactor pressure vessel weld contains a defect of critical size. The number of defects of a given size predicted is compared with existing statistics-on defects. A set of model parameters is selected such that the predictions of the model are consistent with existing statistics. The more sensitive input parameters are determined. Finally, an optimal inspection procedure is suggested. This procedure is based on several assumptions regarding inspection and downtime costs. The calculations are performed for defects under both low and high stress since the development rates and inspection procedures for these two categories are distinctly different.

5.1. Low stress welds

Table 13 summarizes the input data used in figs 5-18 inclusive for welds under low stress (the figures are plotted on linear graph paper). The parameters used in fig. 5 are consistent with the assumed base statistics for nuclear vessels. The base run for low stress welds in nuclear pressure vessels assumed the following input parameters: PA(t = 0) = 6.0 x 10 -4 defects/weld;PB(t = 0) = 6.0 x 10 -6 defects/weld;Pc(t = 0) = 2.0 x 10 -6 defects/weld; PD(t = 0) = 0;HA(Z) = 60.0%, Vi;H/a(Y.) = 90.0%, Vi;HC(Z) = 95.0%, Vi;HD(~) = 99.9%, Vi; W i = 5%, Vi; Qi = 2.0 x 10 -8 defects/weld hr, Vi; kA,i = 2.0 x 10-1/hr, Vi; kB, i = 2.0 x 10-9/hr, Vi; kc,i = 2.0 x 10-a/hr, Vi where Vi = for all i inspections.

According to the model and using the base run parameters, the mean expected number of defects per weld at t = 350 000 hr (i.e. assumed end of vessel life), of sizes A, B, C and D is approximately 3.8 x 10 +2 , 6.7 x 10 -2 , 7.9 x 10 -5 and 6.3 x 10 -7 defects per weld, respectively.


0

<

Z

~,...,

I " ' .0

,< X

x

O0

w~

VV VV

0 0 ~ 0 0

x

VVV

VVV

0 0 0

~') .It- it% to)

0 0 ~ 0 0

0 0 ~ 0 0

0 0 ~ 0 0

0 "WD ~O "It"

~ c5

0

0

0

"el

8

0

0

d~

,m

J

8 X

- t - -

-it.


It would be interesting to compare the predictions of the model with the actual number of defects found. In particular, the UK located three defects of critical size (i.e. size D), in approximately 181 000 low stress welds (during 1.3 x 101 low stress weld hours). Since size D defects are considered to be in the failed state, the probability of finding a size D defect is assumed to be essentially equal to the probability of one existing. According to the British data, the expected D size defect concentration is 1.7 x I 0 -s defects per low stress weld after 1.3 x 10 I weld hours.

EXPECTED NUMBER OF DEFECTS PER WELD

PAlt) PB(t ) Pc(t) PDlt)

' L 104 _ 101 -- 10.3 !_ 10-6

103 100 T O T O + T 1 2 - I i~o'i

12 i0.1 14! 17 - /

101 I0 -2

i too ~0.3 10-6 10-6 - L . I

10.1 10"4 / ~ ~ :

10. 2 : IO "5 10.6 10"9 / '~ " - '

o 'u ~ . S

o I : - ,"

p4" '

100 000 200,000 TIME (HOURS)

I 3O0 000

PD

PA PB PC

Fig. 5. The expected number of defects per weld of sizes A, B, C and D as a function of time. Base run for low stress welds.


PA(t) PB(t) Pc(t) PD(t) /

104 - 101 - 10"3 10"6 h

/ 11~' 1o T O 4

101 10 .2 ,. 4

100 10. 3 J 10"5

10-1 10"4

10 .2 10 .5 10"6

0 100,000 20(] ,000 TIME (HOURS)

300000

PD PA

PB PC

Fig. 6. The expected number of defects per weld of sizes A, B, C and D as a function of time. Shortened inspection intervals for low stress welds.


PA(t)

10 4 .

10 3


PB(t) Pc(t) PD(t)

L 101 10 .3 _ 10 -6 10 0 T o T 0+ T 1

! 10 2 - 10-1 _ 10-4 _ 10-7 _

101 10-2

10 0 10 .3 10 .6 10.8 -

10-I 10-4 . 10-2 10-5 10"6 10-9 '

~6 q

"'1 1 100,000

" """ I, 200,000

TIME (HOURS)

PC

L ~ PD

PA ~" PB p~ d,m

300000

Fig. 7. The expected number of defects per weld of sizes A, B, C and D as a function of time. No defects initially present and no inspections for low stress welds, except for zeroth inspection.

PA(t) PB(t) Pc(t)

10 4 -- 101 - 10"3J--

10 3 10 0


PD(t)

,, t 10 2 - 10-I _ 10-4 ~- 10-7

I

I 101 -- 10-2 100 -- 10-3 10-5 ~- 10 .8

/ 10-1 10-4 10-2 L 10-5 10-6 L_ 10-9

T O TO+ T 1

e,"

0

2 i z. 0

100,000

~ Bo ~ b~

~l ,md

pd

I

200 00O TIME (HOURS)

m,zp am

~o ~d

300000

% PA

Fig. 8. The expected number of defects per weld of sizes A, B, C and D as a function of time. Inspection area increased for low stress welds.



PA(t) PB(t)

10 3 - 10 .21-

10 2 -

1o I - lO "3 I -

lO -

10-1 - 10- 41-

10-2 -

lO.3 _ 1o .6L_

PC ( t ) PD ( t )

X 0 T O + T 1 2 I I I

/ ," I I " 1o-S l i - PD

10"4 -- " PC 8x 10 -9

.,,0,1- I / , . , , r " - I l ,.,:,L I A - I . l _ , . t / ! , , " "

i . . . . . . 10"5 -- 0 r i n, n i , n l 0 100,000 20(] ,000 300,000

TIME (HOURS:

Fig. 9. The expected number of defects per weld of sizes A, B, C and D as a function of time. Inspection area considerably increased for low stressed welds.


PA(t) PB(t) Pc(t) PD(t)

/ I lO 3 T O T 0+T 1 2 | I

o.o5 .~lO-S- 5,10-~- I ~T, I 0,04 4x10- 5 ~- 4x10- 9 -- , ~ '

101 ~' /

o.o, ~,0-5~10-s- I Lf'] i . . ~ I "

I- T- 10" 1 ,,~,6 0.01 lx10 "5 ~ lx10- 9 -- P'* 10-21_ l , ~ ~ ,,,~ ,,,, ,~ o g

Pc

PD

~,~," PB

I 300000 0 100 000 20(1000

TIME (HOURS)

Fig. 10. The expected number of defects per weld of sizes A, B, C and D as a function of time. No defects initially present for low stress welds.



PA(t) PB(t) Pc(t) PD(t)

1012 I 103 100 ~-

I 102 ~- 10"1 , 108 ?

10 4 100 ~ 10"3 ?

10"1 ~ 10"4

10-2 [-- 10-5

O 100,000 200,000 TIME (HOURS)

~,~'~ ~ PB

PD Pc

.~ , , . PA

I

Fig. I 1. The expected number of defects per weld of sizes A, B, C and D as a function of time. Increased generation rate for low stress welds.

PD(t = 350,000 HOURS)

a ,.J ILl ~=r~ ln-5 mm -- mq- Q.

N ~ lO-5 u. I-..

o5

~ 10-7 10-5

I I I 1 I 10-4 10-3 10-2 10 "1 10 0 NUMBER OF DEFECTS PER WELD OF SIZE "A'" AT t = 0 HRS

PA(t - 0 HOURS)

Fig. 12. The number of defects of size D per weld at t --- 350 000 hr as a function of the number of size A defects per weld initially present. All other parameters are fixed as for base run, low stress welds.

The UK data is based almost exclusively on non-nuclear pressure vessel welds which are assumed to be fabricated using less stringent standards than nuclear pressure vessels [10, 23, 24] and have lower inspection requirements [10, 23, 26]. Also, ~he non-nuclear vessels are under a much wider range of pressures [9, 10]. Hence, one might assume that there is a distinct difference in weld quality between the vessel welds studied by Phillip and Warwick and those used in nuclear pressure vessels.

By the end of weld life, there is approximately a 170 x 10-7/6.3 x 10 --/ or about a 27 times higher concentration of D size defects existing in the UK non-nuclear low stress welds than the concentration predicted for US nuclear vessel low stress welds using the model and the assumed base data.


There are a variety of combinations of input parameters that could be changed to increase the predicted defect concentrations in nuclear vessel low stress welds

1-s2.0-0029549375900837-main

Documents

Transcript of 1-s2.0-0029549375900837-main