ASME

CHAPTER

46

46.1 INTRODUCTION

The role of fracture mechanics in Section XI applicationscomes in the form of evaluation of indications or flaws detectedduring inservice inspection of nuclear components. The earlyASME BPVC Section XI evaluation procedures have been typi-cally based on linear elastic fracture mechanics (LEFM). Forexample, the vessel flaw evaluation procedure in IWB-3600 in the1977 edition was based on the LEFM analyses described else-where [1,2]. Appendix G of Section XI (essentially the same asAppendix G of Section III) also is an example of the first use ofLEFM in Section XI applications. The background of AppendixG LEFM technology is provided in WRC-175 [3]. The currentSection XI flaw evaluation procedures (Appendix A) have someprovision for loading with limited plasticity in the form of plasticzone size correction. LEFM is limited by the small-scale yielding(SSY) condition that the plastic zone around the crack tip besmall compared to the size of the K-dominant region and any rel-evant geometric dimension. It is virtually impossible to satisfythis condition for high-toughness, low-strength materials, whichgenerally undergo extensive plastic deformation and crack tipblunting prior to the initiation of crack growth. Crack initiation inthese materials is usually followed by stable crack growth or tear-ing. The need to include the influence of significant plastic defor-mation, which may accompany crack initiation and the subse-quent stable growth, has been the main driving force for thedevelopment of the field of elastic-plastic fracture mechanics(EPFM). Furthermore, higher load capability (over that predictedby LEFM) can be demonstrated in ductile materials by allowinglimited stable crack extension using EPFM techniques. Figure46.1 [4] shows the role of elastic-plastic or nonlinear fracturemechanics; a center-cracked plate loaded to failure is considered.This figure shows a schematic plot of failure stress versus fracturetoughness (KIc). For low toughness materials (such as ferriticsteels at lower shelf), brittle fracture is the governing failuremechanism and the critical stress is predicted by the usual LEFMequations and the material KIc. At very high toughness values,

LEFM is no longer valid and failure (or collapse by limit load) isgoverned by the flow properties of the material. Fracture mechan-ics ceases to be relevant to the problem because the failure stressis insensitive to toughness; a simple limit load analysis is all thatis required to predict failure stress. The appropriate material prop-erty in this case is the flow stress that may be generally taken asthe average of the material yield and ultimate stress or a suitablemultiple (e.g., a factor of 3) of the Code allowable stress, Sm. Atintermediate toughness levels, there is transition between brittlefracture under linear elastic conditions and ductile overload orcollapse. Nonlinear or EPFM bridges the gap between LEFM andcollapse. When the plasticity is limited to a small zone surround-ing the crack tip, an LEFM solution modified by a plastic zonesize is adequate; this zone is called the SSY zone. Some of theferritic materials used in the nuclear pressure vessel applicationsat the upper-shelf temperatures are analyzed using this approachwith the material fracture resistance determined through appropri-ate J integral testing.

46.2 EARLY PROGRESS IN THEDEVELOPMENT OF EPFM

The movement toward the use of EPFM started in the 1960s; theprogress through 1980s is summarized elsewhere [4]. Extracts [4]are presented here to provide the reader a brief background on thedevelopment of EPFM. LEFM ceases to be valid when significantplastic deformation precedes failure. During a relatively short timeperiod (1960–1961), several researchers, including Irvin [5],Dugdale [6], Barenblatt [7], and Wells [8], developed analyticalmethods to correct for yielding at the crack tip. The Irwin plasticzone correction was a relatively simple extension of LEFM, whileDugdale and Barenblatt each developed somewhat more elaboratemodels based on a narrow strip of yielded material at the crack tip.Wells proposed the displacement of the crack faces, the parameternow known as crack tip opening displacement (CTOD), as an alter-native fracture criterion when significant plasticity precedes failure.

APPLICATIONS OF ELASTIC-PLASTIC

FRACTURE MECHANICS IN SECTION XI,ASME CODE EVALUATIONS

Hardayal S. Mehta and Sampath Ranganath

ASME_Ch46_p001-016.qxd 9/27/08 1:32 PM Page 1

2 • Chapter 46

In 1968, Rice [9] developed another parameter to characterizenonlinear material behavior ahead of a crack. By idealizing plas-tic deformation as nonlinear elastic, Rice was able to generalizethe energy release rate to nonlinear materials. He showed thatthis nonlinear energy release rate can be expressed as a line inte-gral, which he called the J integral, evaluated along an arbitrarycontour around the crack. At the time his work was being pub-lished, Rice discovered that Eshelby [10] had previously pub-lished several so called conservation integrals, one of which wasequivalent to Rice’s J integral. Eshelby, however, did not applyhis integrals to crack problems. That same year, Hutchinson [11]and Rice and Rosengren [12] related the J integral to crack tipstress fields in nonlinear materials. These analyses showed thatthe J integral can be viewed as a nonlinear stress intensity para-meter as well as an energy release rate. Rice’s work might havebeen relegated to obscurity had it not been for the activeresearch effort by the nuclear power industry in the UnitedStates in the early 1970s. Because of legitimate concerns forsafety, as well as political and public relations considerations,the nuclear power industry endeavored to apply state-of-the-arttechnology, including fracture mechanics, to the design and con-struction of nuclear power plants. The difficulty with applyingfracture mechanics in this instance was that most nuclear pres-sure vessel steels were too tough to be characterized with LEFMwithout resorting to enormous laboratory specimens. In 1971,Begley and Landes [13], who were research engineers atWestinghouse, came across Rice’s article and decided, despiteskepticism from their coworkers, to characterize fracture tough-ness of these steels with the J integral. Their experiments werevery successful and led to the publication of a standard proce-dure for J testing of metals 10 years later [14]. Material tough-ness characterization is only one aspect of fracture mechanics.To apply fracture mechanics concepts to design or flaw evalua-tion, one must have a mathematical relationship between tough-ness, stress, and flaw size. Although these relationships werewell established for linear elastic problems, a fracture designanalysis based on the J integral was not available until Shih andHutchinson [15] provided the theoretical framework for such anapproach in 1976. A few years later, the Electric PowerResearch Institute (EPRI) published a fracture design handbook[16] based on the Shih and Hutchinson methodology. The

components covered were the basic fracture test specimengeometries; this was followed by solutions for geometries (e.g.,reactor pressure vessels and piping) typical in nuclear industryapplications [17,18]. The applied J integral values wereobtained through an estimation scheme that used material stressstrain characteristics and a tabulated set of coefficients. This isdiscussed further in the next section. In the United Kingdom, theCTOD parameter was applied extensively to fracture analysis ofwelded structures beginning in the late 1960s. While fractureresearch in the United States was driven primarily by the nuclearpower industry during the 1970s, fracture research in the UnitedKingdom was motivated largely by the development of oilresources in the North Sea. In 1971, Burdekin and Dawes [19]applied ideas proposed by Wells [20] several years earlier anddeveloped the CTOD design curve, a semiempirical fracturemechanics methodology for welded steel structures. The nuclearpower industry in the United Kingdom developed their ownfracture design analysis [21], based on the strip yield model ofDugdale and Barenblatt. Shih [22] demonstrated a relationshipbetween the J integral and CTOD, implying that both parame-ters are equally valid for characterizing fracture. The J-basedmaterial testing and the flaw evaluation methodologies devel-oped in the United States and the British CTOD methodologyhave begun to merge in recent years, with positive aspects ofeach approach combined to yield improved analyses. Both para-meters are currently applied throughout the world to a range ofmaterials. A survey paper [23] and another publication [24] pro-vide an excellent description of the advances made in EPFMthrough 1980.

46.3 ENGINEERING APPROACH TO EPFMAND PIPING APPLICATIONS

There are essentially three approaches considered in theapplication of EPFM in flaw evaluations. These approaches arethe following: (a) J-integral tearing modulus–based approachor J-T methodology (b) deformation plasticity failure assess-ment diagram (DPFAD) methodology (c) R-6 methodologyASME BPVC Section XI has considered the first two approachesin the flaw evaluations. All three methodologies consider thecalculation of the J integral, directly or indirectly. Therefore,the engineering estimation of the applied J integral is dis-cussed next.

46.3.1 J Integral Estimation Method As one would guess, many of the problems of practical inter-

est are in the elastic-plastic regime requiring an estimationscheme to calculate the J integral. The elastic-plastic estimationprocedure derives from the work of Shih and Hutchinson [15]and others [25,26]. The elastic and plastic components of J inte-gral are computed separately and added to obtain the total J asfollows:

Jtotal � Jel � Jpl (1)

Figure 46.2 [4] schematically illustrates a plot of J versusapplied load. The material stress-strain behavior in the estima-tion scheme is characterized in the Ramberg-Osgood form asfollows:

(�/�0) � (�/�0) � �((�/�0)n (2)

FIG. 46.1 EFFECT OF FRACTURE TOUGHNESS ON THEGOVERNING FAILURE MECHANISM


COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 3

where

�0 � a reference stress value that is usually equal to the yieldstrength, �0 � �0 /E

E � Young’s modulus � � a dimensionless constantn n � the strain-hardening exponent

Figure 46.3 [27] shows a typical Ramberg-Osgood fit for a car-bon steel material typically used in nuclear applications. Typicalfully plastic equations for J, crack mouth opening displacement(Vp), and load line displacement (�p) would have the followingform in the estimation scheme:

Jpl � � �0 �0 b h1 (a/W, n) (P/P0)n�1 (3)

Vp � � �0 a h2 (a/W, n) (P/P0)n (4)

�p � � �0 a h3 (a/W, n) (P/P0)n (5)

where

b � the uncracked ligament lengtha � the crack length

h1, h2, and h3 � dimensionless parameters that depend ongeometry and strain-hardening exponent; the hfactors for various geometries and n valueshave been tabulated in several EPRI reports[16–18,27]

P � the applied load

The reference load, P0, is usually defined by a limit load solu-tion for the geometry of interest; P0 normally corresponds to theload at which the net cross-section yields. It should be noted thatthe plastic load line displacement, �p, is only that component ofplastic displacement that is due to the crack. The total displace-ment in a structure is the sum of the elastic and plastic crack andno-crack components.

Figure 46.4 shows the analytical expression for the calculationof Jpl for a pipe with a through-wall circumferential crack subject-ed to axial load and/or bending moment. The specific values fordimensionless parameter h1 are given in Table 46.1.

The elastic component of J is computed from the elastic stressintensity factor for an effective crack size as follows:

Jel � {KI2 (aeff)}/E� (6)

where

E� � E for plane stress and E� � E/(1 v2) for plane straincondition; v is the Position’s ratio and is typically assumedequal to 0.3.

The parentheses in the preceding equation indicate that KI is afunction of aeff rather than a multiplication product. The effectivecrack size is determined from the Irwin correction modified toaccount for strain hardening as follows:

aeff � a � {1/[1� (P/P0)2]}{1/(�)}� {(n 1)/(n �1)}{KI(a)/�0}2 (7)

where

� 2 for plane stress � 6 for plane strain conditions

The analytical expressions for KI are available from fracturemechanics handbooks [27]. When J-controlled crack growth isapplicable, the condition for continued crack growth is [28,29] asfollows:

J(a, P) � JR(a a0) (8)

For any given configuration, the crack driving force J is a func-tion of crack length a and load per unit thickness P. The JR curveis a function of the amount of crack growth, �a � (a a0), and isobtained experimentally. Therefore, crack growth is unstable ifthe following applies:

( J/ a)�T dJR/da (9)

The subscript in the preceding equation denotes a partial deriv-ative with the total displacement held fixed. It is convenient in¢T

00

FIG. 46.2 THE EPRI J ESTIMATION SCHEME

FIG. 46.3 TRUE-STRESS TRUE-STRAIN CURVE FOR A333GRADE 6 BASE MATERIAL IN NRC/BCL 4111-1 PIPE


4 • Chapter 46

examining stability to introduce nondimensional tearing moduli[28] as follows:

TJ � {E/�02}( J/ a)�T and TJR � {E/�0

2}(dJR/da) (10)

The instability criterion is then simply phrased in terms ofthese moduli as follows:

TJ � TJR (11)

Figure 46.5 shows the J-T diagram. The predicted instabilityload is shown in Fig. 46.5b.

46.3.2 Application of J-T Approach to AusteniticStainless Steel Piping Flaw Evaluations

Prior to the publication of the BPVC 1983 Addenda, flaw eval-uation procedures in IWB-3600 were applicable to ferritic steelcomponents 4 in. or greater in thickness (based on LEFM). Flawevaluation procedures and allowable flaw sizes for LWRaustenitic piping first appeared in IWB-3640 in that Addenda.The evaluation was based on a plastic collapse failure mechanismand allowable flaw sizes were developed using limit load analysis.Because plastic collapse is the anticipated failure mechanism,

00

secondary stress, such as bending due to thermal expansion, isassumed to be relaxed at failure and only primary membrane andbending stresses were used when performing flaw evaluationsin accordance with IWB-3640. A J-T analysis for assumed

FIG. 46.4 FULLY PLASTIC J INTEGRAL FOR CIRCUMFERENTIAL THROUGH-WALL FLAWS IN CYLINDERS

FIG. 46.5 DETERMINATION OF INSTABILITY J, T, ANDASSOCIATED LOAD FOR LOAD CONTROL EPFM ANALYSIS



through-wall flaw geometries [30] showed that the predictedinstability loads essentially reach those predicted by limit loadand, thus, provided additional technical basis for the limit loadapproach. Figure 46.6 shows an example of this prediction. Forlimit load comparison, the flow stress was assumed as 3Sm, wherethe Sm is the Code-specified allowable stress for the pipe material.Through-wall flaw geometries were assumed. A similar EPFM

evaluation for a weld overlay geometry, where a 360� flaw withdepth equal to the original pipe thickness was assumed, wasreported [31] with the conclusion that limit load conditions areachieved at the cracked section. Subsequently, the need arose todistinguish between high-toughness materials, such as thewrought austenitic material, and certain lower toughness fluxwelds, which include shielded metal arc welds (SMAW) and sub-merged arc welds (SAW). This distinction became necessarybecause some small specimen experimental data suggested thatthe applicable failure mechanism for the flux welds is unstablecrack extension that would occur at loads lower than the plasticcollapse load [32,33]. The approach used was to develop somepenalty factors or so-called Z factors to reduce the allowable flawsize at any specified load for flux welds relative to the high-toughness materials. An EPFM approach was used to develop thesefactors. Figure 46.7 [32] shows an example of this evaluation. The

TABLE 46.1 FULLY PLASTIC J INTEGRAL FOR CIRCUMFERENTIAL THROUGH-WALL FLAWS IN CYLINDERS

FIG. 46.6 COMPARISON OF NET-SECTION COLLAPSELOAD AND ESTIMATION SCHEME MAXIMUM LOAD FORAXIALLY LOADED 304 STAINLESS STEEL PIPE WITHTHROUGH-WALL CIRCUMFERENTIAL CRACK

FIG. 46.7 DETERMINATION OF J AND T AT CRACK INSTA-BILITY FOR AUSTENITIC SAW AT 550�F


6 • Chapter 46

analysis considered a pipe with a through-wall flaw subjected to abending moment.

The ratio of the limit load to the calculated instability load pro-vided the Z factor value. By taking conservative bounds of theinstability load results, the following expressions for Z factorswere developed:

for SMAW, Z � 1.15 [1 � 0.013 (OD-4)] (12)for SAW, Z � 1.30 [1 � 0.010 (OD-4)] (13)

where

OD � the pipe outer diameter in inches Subsequent experimental work by Battelle [34] indicated that

there was no statistically significant difference between the SAWand SMAW J-R curves and, therefore, the 2004 Edition ofAppendix C specifies the SAW Z factor for SMAW also.

Because limit load may not be reached prior to failure, it wasrecommended that the expansion stresses with a margin of 1.0 beincluded along with primary membrane and bending stress whenevaluating flaws in flux welds. The allowable flaw sizes (e.g., inASME BPVC Section XI, Appendix C, 2004 Edition) are present-ed in tabular form as a function of stress ratio. When using theEPFM approach, the stress ratio for a circumferentially flawedpipe is defined as the following:

stress ratio � Z[(�m � �b � �e /SFb)/�f (14)

where

�m � primary membrane stress �b � primary bending stress �e � secondary bending stress �f � material flow stress

SFb � structural factor for bending

Note that the preceding definition of stress ratio is consistentwith the 2002 Addenda of ASME BPVC Section XI. Prior to that,Sm was used instead of �f in developing tables. The structural fac-tor (SF) has the same meaning as the safety factor. The Code iscurrently transitioning from safety factor terminology to structuralfactor to specify the required structural margins.

It should also be noted that, prior to the 2002 Addenda, theallowable circumferential flaws were developed using an SF of2.77 (for normal/upset or Levels A/B conditions) and 1.39 (foremergency/faulted or Levels C/D conditions) on the sum of theprimary membrane and bending stresses. Allowable longitudi-nal flaw sizes were developed using an SF of 3.0 and 1.5 on pri-mary membrane stress for normal/upset and emergency/faultedconditions, respectively. Separate SFs for primary membraneand primary bending and separate SFs for various service levelswere incorporated in the 2002 Addenda. The rationale for thischange was to bring consistency with ASME BPVC Section III.The technical basis for these changes is provided elsewhere[35]. Table 46.2 gives the revised SFs; these SFs are applicableto Classes 1, 2, and 3 piping and to both the austenitic and fer-ritic materials. The flow stress was also redefined from 3Sm tothe average of yield and ultimate stress. Also, the use of actualmaterial properties was allowed where such information isavailable.

The revision of SFs and the definition of flow stress do notdirectly affect the Z factors, because they are based on the ratio tolimit load; however, the allowable flaw depth would be affectedby these changes.

46.3.3 Application of J-T Approach to Ferritic PipingFlaw Evaluations

In 1983, the Working Group on Flaw Evaluation of Section XIinitiated work on the development of flaw evaluation proceduresfor ASME Class 1 ferritic piping. Flawed ferritic piping was rec-ognized to have possible failure mechanisms, which, dependingon operating temperature, could range from linear elastic fractureto elastic-plastic ductile tearing to plastic collapse. This wide vari-ation of failure mechanisms necessitated an evaluation procedurethat could account for all possible failure modes. The ASMESection XI Working Group on Flaw Evaluation approached thisproblem through the development of two separate approaches toaddress the region where EPFM is applicable. The first approachwas similar to the J-T approach used for austenitic piping [36,37].This resulted in the introduction of Code Case N-463 [38] in the1988 Addenda and Nonmandatory Appendix H in the 1989Edition [39]. The other approach, based on the DPFAD, isdescribed in the next section.

As a minimum, the EPFM approach on requires data JIC of thematerial. The evaluation methodology also developed a correla-tion between JIC and the more generally available Charpy V-notch (CVN) absorbed energy. A screening procedure basedon DPFAD method is provided to identify the appropriate failuremode.

Figure 46.8 shows the screening procedure used; the parame-ters are the same as those used in DPFAD. Simply, the parametersKr

� and Sr� are defined as follows:

Kr� � [KI

2/(E�JIC)]0.5 (15)Sr� � (�b � �e)/�b� (16)

The stress intensity factor KI is the sum of the LEFM contribu-tions from applied membrane and bending stresses including �e.The Code Case and the Nonmandatory Appendix of the SectionXI Code provide the appropriate mathematical expressions to cal-culate the values. JIC is the measure of toughness at the onset ofcrack extension. The reference limit load bending stress is calculated using �y as the flow stress. For circumferential flaws, theJIC and �y values (if user-specified values are unavailable) areshown in Table 46.3. The DPFAD assessment curve was generat-ed using a lower-bound, stress-strain curve with the followingvalues of Ramberg-Osgood parameters: � � 2.51, n � 4.2,�0 � 27.1 ksi, and E � 26000 ksi.

A high Kr� value at failure (a point on the failure assessmentcurve) in Fig. 46.8 implies that the associated Sr value is small,indicating small-scale yielding. If a low Kr value is calculated atinitiation, it is an indication that fracture would be predicted near

sb¿

TABLE 46.2 SAFETY/STRUCTURAL FACTORS FOR CIR-CUMFERENTIAL AND AXIAL FLAWS



limit load. Based on this concept, the applicability range of limitload and LEFM were defined by the ratio of Kr

� to Sr�, as shown in

Fig. 46.8.The flow diagram leading to EPFM evaluation option is shown

in Fig. 46.9. The default material properties used in the evaluationand the corresponding Z factor expressions are shown in Table46.3. Figure 46.10 [37] shows the J-T curves associated with twoJIC that were used to generate the mathematical expressions for Zfactors. When user-specified JIC values are available, the resultingZ factors expressions are provided in Table 46.4.

In the ASME BPVC 2002 Addenda, Appendices H and C werecombined into a revised Appendix C. The revision also includedthe incorporation of separate SFs for membrane and bendingloading into the screening criteria evaluations and the mathemati-cal expressions for the calculation of allowable stresses [40].

46.3.4 DPFAD Method The DPFAD procedure uses deformation plasticity solutions

[16,17] for cracked structures in the format of the British CentralElectricity Generating Board’s (CEGB) R-6 two-criteria failureassessment diagram (FAD). In 1990, the Code approved CodeCase N-494 [41] as an alternative procedure for evaluating flawsin light-water reactor (LWR) ferritic piping. The approach was analternate to then Appendix H of Section XI and allowed the userto remove some conservatism in the existing procedure by allow-ing the use of pipe-specific material properties. The technicalbasis was documented in several technical papers authored byJ.M. Bloom and coworkers [42-45].

The general DPFAD procedure involves the following threesteps [45]:

(a) The generation of the DPFAD curve from elastic-plasticanalysis of a flawed structure using deformation plasticitysolutions for a simple power law strain hardening materialbased on the Ramberg-Osgood stress-strain equation. If theJ-integral response of the structure can be represented bythe following:

Japplied � JIe � Jp (17)

then the following applies:

[Japplied/G] � 1Kr2 � (JI

e � Jp)/G

where

Sr � the ratio of applied stress to net section plastic col-lapse stress

G = KI2/E�

The difference between JIe and G is that JI

e includes thesmall-scale, yielding plastic zone correction while G doesnot. The resulting expression defines a curve in the Kr � Sr

plane, which is a function of flaw geometry, structural

Kr = 2(G/Japplied) = f(Sr)

TABLE 46.3 DEFAULT MATERIAL PROPERTIES AND ZFACTORS FOR FERRITIC PIPING WITH CIRCUMFEREN-

TIAL FLAWS

FIG. 46.8 DPFAD FOR FAILURE MODE SCREENING CRITERION


8 • Chapter 46

FIG. 46.9 FLOW CHART FOR SCREENING CRITERIA TOESTABLISH THE ANALYSIS METHOD

FIG. 46.10 FERRITIC MATERIAL J-T CURVES USED IN EPFMEVALUATION

TABLE 46.4 Z FACTORS FOR CIRCUMFERENTIAL FLAWS IN FERRITIC PIPING WITH USER-SPECIFIED MATERIAL PROP-ERTIES

configuration, and stress-strain behavior of the materialdefined uniquely by � and n. Because both Kr and Sr are lin-ear in applied stress, the DPFAD curve is independent ofthe magnitude of the applied loading.

(b) The determination of assessment points based the ratio ofKI or √ of the structure divided by the relevant materi-al property √ or at flaw initiation or for stable1JIC1KIC

1JI



crack growth, , the tearing resistance of the mate-rial for the ordinate, Kr�, and the ratio of the applied stress(load) to net section plastic collapse (limit load) for theabscissa, Sr�. For flaw initiation, a single assessment pointis calculated. For stable crack growth, a locus of assessmentpoints are determined by incrementing the crack size a bya � �a in the calculation of JI for a constant applied load.The resulting locus is shown in Fig. 46.11 in the shape of acandy cane.

(c) Crack initiation or tearing instability can be determinedgraphically by plotting the calculated assessment point(s)on the FAD. For crack initiation, the single assessmentpoint must fall on the DPFAD curve or inside the curve. Fortearing instability, the critical instability load is determinedby the tangency of the assessment locus with the DPFADcurve, as shown in Fig. 46.11. Any assessment point on aline from the origin of the diagram is directly proportionalto load with any other point on that same line, and only oneload level is needed to determine the instability load. Theinstability load is determined by multiplying the appliedload by the ratio of the distance from the origin to the pointof intersection of the line with the DPFAD curve to the dis-tance from the origin of the diagram to the applied loadpoint. Work is in progress to revise the Sr cut-off to be con-sistent with Appendix C.

The original Code Case N-494 was further revised in 1994 toinclude assessment of austenitic piping where the material stress-strain behavior cannot be fit to the Ramberg-Osgood model[46,47]. This Code Case has been revised in 2007 to incorporatethe impact of separate safety factors for membrane and bendingstresses. The 2002 Addenda to ASME BPVC Section XI also cre-ated a new Nonmandatory Appendix H covering the DPFADmethodology (the old Appendix H was folded into a revisedAppendix C).

1Jg(¢a) 46.3.5 R-6 Method and EPFM in Non-U.S. Codes andStandards

The British R-6 method was used as the initial framework ofthe DPFAD method. The first R-6 document [21] emerged in1976 as a result of a requirement of the Central ElectricityGenerating Board in the United Kingdom to include the assess-ment of fracture resistance in the design of steam-generatingheavy-water reactor (SGHWR), which was being considered atthat time for commercial operation. The last major revision of R-6was in 1986 [48]. Recently, developments in fracture mechanicsmethodology, in particular the procedure resulting from theEuropean project SINTAP, the British Standards Guide BS7910,and the American Petroleum Institute document API 579, stimu-lated the decision to revise R-6 in its entirety as the new Revision4 [49]. Other work of interest related to EPFM is the Swedish SKIwork [50,51].

46.4 APPLICATION TO RPV EVALUATION

The EPFM has been applied to RPV evaluation in three distinctways: upper-shelf energy evaluation, the new Section XI flawevaluation approach, and a probabilistic approach.

46.4.1 LOW UPPER-SHELF ENERGYEVALUATION

One of the first applications of EPFM for pressure vessels wasin addressing the resolution of the low upper-shelf toughnessissue. Appendix G of 10 CFR Part 50 [52] requires that “reactorvessel beltline materials must have Charpy upper-shelf energy ofno less than 75 ft-lb (102 J) initially and must maintain upper-shelf energy (USE) throughout the life of the vessel of no lessthan 50 ft-lb (68 J),” unless it is demonstrated that lower upper-shelf energy will provide safety margins equivalent to thoserequired by ASME BPVC Appendix G [53]. It was found thatvessels welded with the Linde 80 weld material did not alwaysmeet the regulatory requirement of 50 ft-lb. The problem of evalu-ating materials that did not meet the regulatory requirement of 50ft-lb was designated as Unresolved Safety Issue A-11. The resolu-tion of USI A-11 was documented by the U.S. NRC in NUREG-0744, Resolution of the Task A-11 Reactor Vessel MaterialsToughness Safety Issue [54]. Although NUREG-0744 providedmethods for evaluating the fracture behavior of these materials, itdid not provide specific criteria for demonstrating the equivalenceof margins with Appendix G of the ASME Code. This was subse-quently developed by the ASME Section XI Subgroup onEvaluation Standards and then issued as Appendix K of SectionXI [55]. The U.S. NRC approved Appendix K but provided guid-ance acceptable to the NRC staff for evaluating pressure vesselsthat did not meet the 50 ft-lb regulatory requirement inRegulatory Guide 1.61 [56].

46.4.1.1 Appendix K Criteria. Appendix K specifies differentrequirements for Levels A/B conditions and Levels C and D con-ditions, as summarized below:

(a) Level A/B Conditions. When the upper-shelf Charpy energyof the base metal is less than 50 ft-lb, both axial and cir-cumferential interior flaws are postulated. These are evalu-ated using the toughness properties for the corresponding

FIG. 46.11 INSTABILITY POINT DETERMINATION INDPFAD SPACE


10 • Chapter 46

orientation. A semielliptical surface flaw with an a/t � 0.25and with an aspect ratio of 6-to-1 surface length to flawdepth is postulated. A smaller flaw size may be used on anindividual case if the basis is justified. Two criteria must besatisfied as described below: the crack driving force mustbe shown to be less than the material toughness, as given bythe following equations:

Japplied � J0.1 (18)

where

Japplied � the J-integral value calculated for the postulated flawunder pressure and thermal loading, where theassumed pressure is 1.15 times the maximum accumu-lation pressure, with thermal loading using the plant-specific heatup and cooldown conditions.

J0.1 � the J-integral characteristic of the material’s resis-tance to ductile tearing (Jmaterial), as denoted by a J-Rcurve test at a crack extension of 0.1 in.

�Japplied/�a � �Jmaterial/�a, with load held constant at Japplied � Jmaterial (19)

where

Japplied � the J-integral value calculated for the postulated flawunder pressure and thermal loading, where the assumed pressureis 1.25 times the maximum accumulation pressure, with thermalloading.

The first criterion is based solely on limited ductile crackextension (initiation). The second criterion is based on flaw stabil-ity, in which case ductile stable tearing is considered. The J-Rcurve used in the analysis must be a conservative bound of the J-Rdata representative of the vessel material.

(b) Level C Conditions. For Level C conditions, the postulat-ed flaw is somewhat smaller: 0.1 times the thickness plusclad thickness but not more than 1 in. and aspect ratio a/�� 1/6. The initiation and stability criteria are the same asthose in Eqs. (1) and (2), except that the Japplied is

calculated for the governing Level C loading conditions(i.e., factor one on pressure and thermal stresses). Thelower factor is justified based on the fact that Level C rep-resents lower probability events. Also, the J-R curve usedin the analysis must be a “conservative representation” ofthe vessel material.

(c) Level D Conditions. For Level D conditions, the postulatedflaw is the same as that for Level C: 0.1 times the thicknessplus clad thickness but not more than 1 in. and aspect ratioa/� �1/6. There is no criterion for ductile crack extension(initiation) but there is a criterion for crack stability. Thestability requirement of Eq. (19) applies with Japplied beingcalculated for the governing Level D loading conditions(i.e., factor one on pressure and thermal stresses). Thelower factor is justified based on the fact that Level D rep-resents the lowest probability events. Also, the J-R curveused in the analysis must be a “best estimate representa-tion” of the vessel material. In addition to the flaw stabilityrequirement, the stable flaw depth must not exceed 0.75times the wall thickness and the remaining ligament mustbe safe from tensile instability.

Table 46.5 summarizes the different requirements for the differ-ent conditions: Levels A/B, Level C, and Level D for the lowupper-shelf evaluation.

The technical basis for Appendix K is described in detail inWRC Bulletin 413 [57]. Specifically, it describes the procedure forcalculating Japplied and three methods for the stability evaluation.

46.4.1.2 Evaluation Procedure for the Calculation of Japplied.The calculation of Japplied assumes small-scale yielding. The firststep is the calculation of K for pressure {KIp(a)} and thermal{KIt(a)} loading for the postulated flaw. The elastic K calculationscan be performed using the equations in Appendix K or other frac-ture mechanics solutions. The effective flaw depth, ae, for small-scale yielding is determined by adding the plastic zone size to thepostulated flaw size as follows:

ae � a � (1/(6�))[(KIp(a) � KIt(a))/�y]2 (20)

where

TABLE 46.5 APPENDIX K REQUIREMENTS FOR DIFFERENT CONDITIONS



a � the postulated flaw depth (inches)KIp and KIt � ksi

�y � the yield strength (ksi)

The effective stress intensity factor Ke � KIp(ae) � KIt(ae) isdetermined by substituting ae in place of a. The applied J forsmall-scale yielding is given by the following:

J � 1000 Ke2 [E/(1 v2)] (21)

where

J � in.-lb/in.2

E � Young’s modulus (ksi) v � Poisson’s ratio

The J integral (JI) for the 0.1-in. flaw extension is given by usingEq. (4) and the appropriate factor on stress (e.g., 1.15 on pressurestress and 1 on thermal stress for Levels A/B conditions). The flawdepth is set at 0.25t � 0.1 in. for Levels A/B conditions; the appro-priate acceptance criterion for ductile crack extension is JI � J0.1.

46.4.1.3 Evaluation Procedure for Flaw Stability Analysis.WRC Bulletin 413 describes three ways to perform the stabilityanalysis.

(a) J-R Curve-Crack Driving Force Diagram Procedure.Figure 46.12 shows the concept of ductile crack extensionand crack stability evaluation. The applied J is calculatedfor a series of crack depths corresponding to increasing lev-els of crack extension. For Levels A/B conditions, a factorof 1.25 on pressure is used. The applied J is plotted againstcrack depth. As shown in Fig. 46.12, the material J-R curveis superposed. Flaw stability at a given applied load isdemonstrated when the slope of the applied J curve is lessthan the slope of J-R curve at the point where the twocurves intersect.

(b) Failure Assessment Diagram Procedure. The DPFAD for aquarter T flaw is shown in Fig. 46.13. The DPFAD plots therelationship between Kr (square root of the ratio of the elas-tic J and the elastic-plastic J) and Sr (ratio of the actualpressure to the limit pressure). The structural factor on pres-sure is determined by scaling distances along a line through

>

1inch

the origin and the assessment point. The pressure is multi-plied by 1.25 when the assessment points are calculated andplotted on the DPFAD. The acceptance criterion for flawstability is satisfied when the assessment points lie insidethe DPFAD curve.

(c) J-Integral/Tearing Modulus (J-T) Procedure. Figure 46.14shows a schematic plot of the J-T curve. The J-T procedureconsists of the following steps:

FIG. 46.12 DUCTILE CRACK GROWTH STABILITY EVAL-UATION

FIG. 46.13 DPFAD FOR A 1/4 T FLAW

FIG. 46.14 THE J INTEGRAL-TEARING MODULUS (J-T)PROCEDURE


12 • Chapter 46

(1) Determine the material J-T curve. (2) Calculate the value of J at the onset of instability (intersec-

tion of the applied J-T and material J-T curve). (3) Calculate the internal pressure at the point of flaw insta-

bility. (4) Apply the acceptance criteria.

46.4.1.4 Guidance on the Material J-R Curve. The generic J-integral fracture resistance curve equation is given in RG 1.161[56] as follows:

JR � (MF){C1(�a)C2 exp[C3(�a)C4]} (22)

The values for C1, C2, C3, and C4 are based on correlationsdeveloped by Eason et al [58]. For generic reactor pressure welds,RG 1.161 provides the values of various constants in the preced-ing equation. For analyses addressing Service Levels A, B, and C,the factor MF was set as 0.629. For analyses addressing ServiceLevel D, the value of MF was set as 1.0. Table 46.6 gives the val-ues for other materials such as the Linde 80 flux welds and reac-tor pressure vessel plate materials.

C1 � exp[4.12 � 1.49 ln (CVN) 0.00249T] (23)

C2 � 0.077 � 0.116 ln C1 (24)

C3 � 0.0812 0.0092 ln C1 (25)

C4 � 0.5 (26)

CVN is the Charpy USE in ft-lb and T is the crack tip tempera-ture in �F. Note that the equations for C2, C3, and C4 are the samefor all materials. In the application of the JR formulation in Eq.(5), CVN is the irradiated USE. This may be available from sur-veillance specimen testing or, alternatively, the values can be esti-mated from RG 1.99, Revision 2 [59], which provides the rela-tionship of USE to crack tip fluence. The alternative relationshipbetween the irradiated USE and the unirradiated USE and fluenceis provided elswhere [7].

Mehta [60] and Griesbach and Smith [61] provided examplesfor the use of Appendix K in evaluating reactor vessels with lowupper-shelf toughness. An important thing to remember is thatAppendix K considers postulated flaws not actual flaws. Its intentis only to determine whether adequate structural factors can bemaintained even in the low USE condition and with rather largeflaw postulates.

46.4.2 New Section XI Approaches for EPFMEvaluation

ASME BPVC Section XI procedures for vessel flaw assess-ment are based on LEFM evaluation. The LEFM methods may besometimes overly conservative and may underestimate the actualmargin, particularly for upper-shelf condition when the deforma-tion behavior is ductile. ASME BPVC Section III recognizes theinherent ductile nature of pressure vessel behavior by excludingsecondary stresses (displacement-governed stresses such as ther-mal and discontinuity stresses) from explicit stress limits (the 3Sm

limit on secondary stress range is related to shakedown andfatigue, not to ductile failure.) Appendix G and the recentAppendix K also recognize the inherent differences between ther-mal and pressure stresses by assigning structural lower factors forthermal stresses. ASME is in the process of developing alternateacceptance criteria based on EPFM techniques. The proposedCode Case N-XXX, Alternative Acceptance Criteria andEvaluation Procedure for Flaws in Ferritic Steel ComponentsOperating in the Upper Shelf Range [62], has been approved bythe ASME Section Subgroup on Evaluation Standards and is nowbeing considered by the Section XI Subcommittee. Because of theimportance of this Code Case and the fact that it represents asignificant change in the technical approach to flaw evaluation,the Code Case criteria and the technical basis are described indetail here.

46.4.2.1 Background. The ASME Section XI flaw evaluationrules for vessels (IWB-3600 plus Appendix A) are based on LEFMtechniques and were developed primarily for the irradiated RPVbelt-line region and other low-temperature carbon and low-alloysteel applications in which the material exhibits limited or no duc-tility. There are situations in which ferritic steel componentsoperate at the upper-shelf region and, therefore, exhibit ample duc-tility. Application of LEFM techniques to these Cases is veryconservative. This Code Case proposes alternate acceptancecriteria for situations in which the component is operating in the upper-shelf temperature region and, therefore, possesses adequateductility to allow the use of EPFM techniques.

46.4.2.2 Technical Approach. EPFM is a more appropriatefracture mechanics technology than LEFM for nonirradiated mate-rials at higher temperatures, such as normal operating conditionsfor both PWRs and BWRs. In the proposed Code Case, both stable

TABLE 46.6 RECOMMENDED J-R CURVE PARAMETERS FROM RG 1.161JR � (MF){C1(�a)C2 exp[C3(�a)C4]}



ductile crack extension and flaw stability due to ductile tearing areconsidered to ensure that crack extension, even for a stable flaw, islimited.

(a) Basis for the Use of EPFM. Ample precedent exists inASME BPVC Section XI for the application of EPFM tomaterials that exhibit some ductility. Such precedent maybe seen in Appendix C for evaluation of flaws in austeniticpiping and ferritic piping and in Appendix K for the assess-ment of RPVs with low upper-shelf toughness. Appendix Cincludes a screening criterion to determine which regime aferritic piping flaw evaluation must consider (LEFM, EPFM,or limit load), and, for the problems that fall into the EPFMregime, specifies different structural factors for primarystresses ( 3) than for secondary loadings (1). An evenmore appropriate approach is presented in Appendix K; inaddition to different structural factors for primary versussecondary loadings, this appendix also provides an approx-imate procedure for performing flaw instability analysis forflaws in RPV materials operating at the upper shelf. TheEPFM approach proposed in this Code Case is very similarto that in Appendix K of Section XI, and, in that sense, theuse of the EPFM techniques proposed for this Code Case isnot unprecedented, except that these techniques are appliedto actual flaws rather than hypothetical flaws.

(b) Determination of Upper-Shelf Temperature. For use of thisCode Case, it must be demonstrated that the vessel materi-al is operating within the upper-shelf range of its Charpyenergy curve. This Code Case requires that the operatingtemperature must exceed the upper-shelf, trigger-pointtemperature, Tc, defined as RTNDT � 105�F. The definitionensures that the material exhibits ample ductility in thicksections and, under applied loading, allows the use ofEPFM techniques.

(c) Loads and Stresses. All primary stresses (i.e., from pres-sure and mechanical loads) and secondary and peak stress-es (i.e., thermal, residual, and highly localized stresses) areto be considered in applying this Code Case. This is con-sistent with the present procedure for flaw evaluation invessels in Section XI, IWB-3600, and Appendix A.

46.4.2.3 Evaluation Procedure. The following analytical pro-cedure must be used:

(a) Applicability of this procedure and acceptance criteria is limited to ferritic steel components on the upper shelf of the Charpy energy curve. The temperature of theoperating condition must exceed the upper-shelf triggertemperature, defined as Tc � RTNDT � 105�F. The effect ofradiation embrittlement must be considered in determin-ing RTNDT.

(b) The flaws must be characterized in accordance with therequirements of IWA-3300, including the proximity rulesof IWA-3300. The flaws must be projected in both axialand circumferential orientations, and each orientation eval-uated.

(c) A flaw growth analysis must be performed to determinethe maximum amount of crack propagation due to fatigue,stress corrosion cracking, or both mechanisms whenapplicable, during a specified evaluation period.

(d) All applicable loading (primary and secondary) must beevaluated, including weld residual stresses, in calculatingthe crack growth and determining flaw acceptability.

'

46.4.2.4 Acceptance Criteria. Two alternate acceptance criteriaare proposed in this proposed Code Case. The first criterion isbased solely on limited ductile crack extension (initiation). Thiscriterion does not consider stable ductile tearing and, therefore, isconservative. It does offer simplicity in the evaluation process forcases where the material is relatively tough or the applied loads arerelatively small. The second criterion is based on flaw stability, inwhich case ductile stable tearing is considered. A flaw is accept-able for continued operation if the J integral (J) satisfies either ofthe criteria below. For all evaluations, the J-integral resistance ver-sus flaw extension curve must be a conservative representation forthe vessel material at the flaw location.

(a) Acceptance Criteria Based Solely on Limited Ductile CrackExtension

(1) Normal/Upset Conditions. J must be evaluated at loadsequal to 3.0 times the primary loads and 1.0 times thesecondary loads, including thermal and residual stress-es. The applied J must be less than the J integral of thematerial at a ductile flaw extension of 0.10 in.

(2) Emergency and Faulted Conditions. J must be evaluatedat loads equal to 1.5 times the primary loads and 1.0times the secondary loads, including thermal and resid-ual stresses. The applied J must be less than the J inte-gral of the material at a ductile flaw extension of 0.10 in.

(b) Acceptance Criteria Based Solely on Limited DuctileCrack Extension and Instability

(1) Normal/Upset Conditions

(a) For ductile crack extension, J must be evaluated atloads equal to 1.5 times the primary loads and 1.0times the secondary loads, including thermal andresidual stresses. The applied J must be less thanthe J integral of the material at a ductile flaw exten-sion of 0.10 in.

(b) For flaw instability due to ductile tearing, theapplied J must be evaluated at loads equal to 3times primary loads and 1.0 times secondaryloads, including thermal and residual stresses. Theapplied J must be less than the predicted instabilitypoint, as shown in Fig. 46.14.

(2) Emergency/Faulted Conditions

(a) For ductile crack extension, J must be evaluated atloads equal to 1.25 times the primary loads and 1.0times the secondary loads, including thermal andresidual stresses. The applied J must be less thanthe J integral of the material at a ductile flawextension of 0.10 in.

(b) For flaw instability due to ductile tearing, theapplied J must be evaluated at loads equal to 1.5times primary loads and 1.0 times secondaryloads, including thermal and residual stresses. Theapplied J must be less than the predicted instabilitypoint determined as shown in Fig. 46.14.

46.4.2.5 Justification for the Structural Factors. The LEFMmethodology treats all loadings on the vessel equivalently, apply-ing equal structural factors ( 3 for normal and upset loads) to bothprimary stresses due to internal pressure and mechanical loads aswell as to secondary and peak stresses, such as those caused by

'


14 • Chapter 46

differential thermal expansion and residual stresses. These load-ings are equivalent in their potential to produce fracture in only themost brittle of materials, such as glass; RPV beltline materials atlow temperatures after significant irradiation embrittlement; andthick, ferritic materials at very low temperatures.

In the EPFM evaluation in Appendix K, structural factors of 3 onprimary loads and 1 on secondary loads are applied. However, itmust be recognized that Appendix K is not dealing with flaw evalu-ations, rather with demonstrating adequate levels of toughness, and,in so doing, it postulates very large hypothetical flaw sizes. ThisCode Case deals with realistic flaw sizes that might potentially beexpected to occur in vessels. Therefore, more conservative structur-al factors, paralleling those in ASME BPVC Section XI, AppendixC, are deemed appropriate. Similar to Section XI, Appendix C, thisCode Case proposes different structural factors for normal/upsetconditions and emergency/faulted conditions.

Different structural factors are also proposed for flaw instabilityand limited ductile crack extension. Because in an EPFM evalua-tion, failure is predicted at instability, higher structural factors areapplied for this condition and lower structural factors are appliedwhen considering limited ductile crack extension.

(a) Normal/Upset Conditions. For the acceptance criterionbased solely on limited ductile crack extension, structuralfactors of 3 for primary loads and 1.0 for secondary andpeak loads (including residual stresses) are proposed. Notethat these are more conservative than the structural factorsactually specified for primary and secondary loads inAppendix K of 1.5 for primary loads and 1.0 for secondaryloads. The proposed structural factor of 1.0 on secondaryloads is also consistent with that specified in Section XI,Appendix C for secondary loads.

For the acceptance criterion based on flaw instability,structural factors of 3 for primary loads and 1.0 for sec-ondary and peak loads (including residual stresses) areproposed. For this Code Case also, a check is made on lim-ited ductile crack extension with structural factors of 1.5for primary loads and 1.0 for secondary loads to ensurethat crack extension is not excessive. Because failure is notassociated with ductile crack extension, these structuralfactors are deemed to be appropriate.

(b) Emergency/Faulted Conditions. For the acceptance criterionbased solely on limited ductile crack extension, structural fac-tors of 1.5 on primary loads and 1.0 on secondary and peakloads are proposed. This is consistent with the structural fac-tors for EPFM evaluations in Appendix C of Section XI.

For the acceptance criterion based on flaw instability,structural factors of 1.5 for primary loads and 1.0 for sec-ondary and peak loads (including residual stresses) areproposed. For this Code Case also, limited ductile flawextension, structural factors of 1.25 on primary loads and1.0 on secondary loads are proposed. Once again, theselower safety factors for limited ductile crack extension arejustified because limited stable ductile extension does notconstitute failure.

46.4.2.6 J-Integral Material Resistance Curve. The use ofEPFM as a basis for acceptance criteria requires adequate charac-terization of the J-integral resistance curve for the vessel material.Section XI, Appendix K specifies three methods for selection ofthe material J-integral resistance curve. A J-R curve may be gen-erated by actual testing of the material, following accepted test

procedures; it may be generated from a J-integral databaseobtained from the same class of material with the same orientation;or an indirect method of estimating the J-R curve may be used,provided the method is justified for the material. This Case pro-poses the same three methods for determining the J-R curve as inSection XI, Appendix K.

46.4.2.7 Conclusion. The proposed Code Case provides alternatecriteria for using EPFM methodology for the evaluation of flaws dis-covered in ferritic steel components, which have been clearlydemonstrated to operate in the upper-shelf temperature range. Thetechnical requirements in this Code Case are very similar to those inSection XI, Appendix K, which allows the use of EPFM techniquesfor RPVs with low upper-shelf toughness. Structural factors consis-tent with other provisions in Section XI, which allow the use ofEPFM for actual flaws, are proposed in this Code Case.

It is expected that the proposed Code Case will reduce theexcess conservatisms inherent in present flaw evaluation method-ologies in Section XI and allow for more appropriate flaw evalua-tion procedures for vessels that operate in the upper-shelf temper-ature range.

46.4.3 Probabilistic EPFMThe nuclear industry is increasingly using probabilistic analysis

and risk-informed evaluation to optimize inspections of pressurevessel and piping inspections. The risk-informed analysis methodol-ogy and application have been defined and approved by the ASMECode and the U.S. NRC. Most of the risk-informed fracturemechanics evaluations have been based on LEFM analysis. Withgreater acceptance of EPFM and risk-informed analysis, it is reason-able to expect that, at some point in the future, probabilistic EPFMevaluations will be used to assess the effectiveness of inspections.

Rahman [63] described a probabilistic model for predictingelastic-plastic fracture initiation in piping with part through finitelength circumferential cracks in piping, using J-integral–basedEPFM methods and standard methods of structural reliability the-ory. The model uses a deformation plasticity–based J-integralanalysis and incorporates a local reduced thickness analogy forsimulating system compliance due to the presence of a crack.Analytical equations are developed to predict the J integral for asurface-cracked pipe under pure bending. The models werequalified by comparison with finite element calculations of the Jintegral. Statistical representation of the uncertainties in loads,crack size, loads, and material properties, were used in conjunc-tion with first- and second-order reliability methods. The statisti-cal distribution of the initial flaw was not based on in-serviceinspection data. Instead, it was assumed that the crack length anddepth would follow a Gaussian probability distribution. The sta-tistical parameters and their probability distribution were arbitraryand the intent was to illustrate the methodology. For a givenapplied moment, the J distribution was calculated both by theapplication of the second-order reliability method and by MonteCarlo simulation. The results indicated that the reliability theorywas consistent with the Monte Carlo simulation.

46.5 REFERENCES

1. Maccary RR. Nondestructive Examination Acceptance Standards –Technical Basis and Development of Boiler and Pressure Vessel Code,ASME Section XI, Division 1 (EPRI Report NP-1406-SR). Palo Alto,CA: Electric Power Research Institute; 1980.



2. Flaw Evaluation Procedures: ASME Section XI (EPRI Report NP-719-SR). Palo Alto, CA: Electric Power Research Institute; 1978.

3. WRC Bulletin 175, PVRC Recommendations on ToughnessRequirements for Ferritic Materials. New York: Welding ResearchCouncil; 1972.

4. Anderson TL. Fracture Mechanics – Fundamentals and Applications.Boca Raton, FL: CRC Press; 1995, 2005.

5. Irwin GR. Plastic Zone Near a Crack and Fracture Toughness.Sagamore Research Conference Proceedings 1961;4.

6. Dugdale DS. Yielding in Steel Sheets Containing Slits. Journal of theMechanics and Physics of Solids 8:100–104.

7. Barenblatt GI. The Mathematical Theory of Equilibrium Cracks inBrittle Fracture. In: Advances in Applied Mechanics, Vol. VII.Academic Press; 1962: pp. 55–129.

8. Wells AA. Unstable Crack Propagation in Metals: Cleavage and FastFracture. Proceedings of the Crack Propagation Symposium, Vol. 1,Paper 84. Cranfield, UK; 1961.

9. Rice JR. A Path Independent Integral and the Approximate Analysisof Strain Concentration by Notches and Cracks. Journal of AppliedMechanics 1968;35:379–386.

10. Eshelby JD. The Continuum Theory of Lattice Defects. Solid StatePhysics 1956;3.

11. Hutchinson JW. Singular Behavior at the End of a Tensile Crack Tipin a Hardening Material. Journal of Mechanics and Physics of Solids1968;16:13–31.

12. Rice JR, Rosengren GF. Plane Strain Deformation Near a Crack Tipin a Power Law Hardening Material. Journal of Mechanics andPhysics of Solids 1968;16:1–12.

13. Begley JA, Landes JD. The J-Integral as a Fracture Criterion (ASTMSpecial Technical Publication 514). West Conshohocken, PA:American Society for Testing and Materials; 1972: pp. 1–20.

14. ASTM E 813-81, Standard Test Method for JIc, a Measure of FractureToughness. West Conshohocken, PA: American Society for Testingand Materials; 1981.

15. Shih CF, Hutchinson JW. Fully Plastic Solutions and Large ScaleYielding Estimates for Plane Stress Crack Problems. Journal ofEngineering Materials and Technology 1976;98:289–295.

16. Kumar V, German MD, Shih CF. An Engineering Approach forElastic-Plastic Fracture Analysis (EPRI Report NP-1931). Palo Alto,CA: Electric Power Research Institute; 1981.

17. Kumar V, et al. Advances in Elastic-Plastic Fracture Analysis (EPRIReport NP-3607). Palo Alto, CA: Electric Power Research Institute;1984.

18. Kumar V, German MD. Elastic-Plastic Fracture Analysis of Through-Wall and Surface Flaws in Cylinders (EPRI Report NP-5596). PaloAlto, CA: Electric Power Research Institute; 1988.

19. Burdekin FM, Dawes MG. Practical Use of Linear Elastic andYielding Fracture Mechanics with Particular Reference to PressureVessels. Proceedings of Institute of Mechanical EngineersConference, London, May 1971, pp. 28–37.

20. Wells AA. Application of Fracture Mechanics at and Beyond GeneralYielding. British Welding Journal 1963;10:563–570.

21. Harrison RP, Loosemore K, Milne I. Assessment of the Integrity ofStructures Containing Defects (Central Electricity Generating BoardReport R/H/R6). 1976.

22. Shih CF. Relationship Between the J-Integral and the Crack OpeningDisplacement for Stationary and Extending Cracks. Journal ofMechanics and Physics of Solids 1981;29:305–326.

23. Kanninen MF, Popelar CH, Broek D. A Critical Survey on theApplication of Plastic Fracture Mechanics to Nuclear Pressure Vesselsand Piping. Nuclear Engineering and Design 1981;67:27–55.

24. Kanninen MF, Popelar CH. Advanced Fracture Mechanics. OxfordScience Publications; 1985.

25. Bucci RJ, Paris PC, Landes JD, Rice JR. J-Integral EstimationProcedures (ASTM Special Technical Publication 514). WestConshohocken, PA: American Society for Testing and Materials;1972: pp. 40–69.

26. Rice JR, Paris PC, Merkle JG. Some Further Results on J-IntegralAnalysis and Estimates (ASTM Special Technical Publication 536).West Conshohocken, PA: American Society for Testing and Materials;1973: pp. 231–245.

27. Zahoor A. Ductile Fracture Handbook, Vol. 1: CircumferentialThroughwall Cracks (EPRI Report NP-6301-D). Palo Alto, CA:Electric Power Research Institute; 1989.

28. Paris PC, Tada H, Zahoor A, Ernst H. The Theory of Instability of theTearing Mode of Elastic-Plastic Crack Growth. In: Elastic-PlasticFracture (ASTM Special Technical Publication 668). WestConshohocken, PA: American Society for Testing and Materials;1979: pp. 65–120.

29. Hutchinson JW, Paris PC. Stability Analysis of J-Controlled CrackGrowth. In: Elastic-Plastic Fracture (ASTM Special TechnicalPublication 668). West Conshohocken, PA: American Society forTesting and Materials; 1979: pp. 37–64.

30. Ranganath S, Mehta HS. Engineering Methods for the Assessment ofDuctile Fracture Margin in Nuclear Power Plant Piping. In: Elastic-Plastic Fracture: Second Symposium, Volume II – Fracture ResistanceCurves and Engineering Applications (ASTM Special TechnicalPublication 803, Vol. 2). West Conshohocken, PA: American Societyfor Testing and Materials; 1983: pp. 309–330.

31. Mehta HS. J-Integral Analysis of Ductile Fracture Margin in PipingWeld Overlays. Transactions of the Ninth International Conference onStructural Mechanics in Reactor Technology 1987;G:469–474.

32. EPRI Report NP-4690-SR, Evaluation of Flaws in Austenitic SteelPiping. Palo Alto, CA: Electric Power Research Institute; 1986.

33. Evaluation of Flaws in Austenitic Steel Piping: Section XI TaskGroup for Piping Flaw Evaluation, ASME Code. Journal of PressureVessel Technology 1986;108:352–366.

34. Ghadiali N, Wilkowski GM. Fracture Mechanics Database forNuclear Piping Materials (PIFRAC). In: ASME PVP Vol. 324,Fatigue and Fracture, Vol. 2. New York: American Society ofMechanical Engineers; 1996; pp. 77–84.

35. Cipolla RC, Scarth DA, Wilkowski GM, Zilberstein VA. TechnicalBasis for Proposed Revision to Acceptance Criteria for ASMESection XI Pipe Flaw Evaluation (ASME PVP Vol. 422). New York:American Society of Mechanical Engineers; 2001: pp. 31–51.

36. Zahoor A, Gamble RM, Mehta HS, Yukawa S, Ranganath S. Evaluationof Flaws in Carbon Steel Piping (EPRI Reports NP-4824M and NP-4824SP). Palo Alto, CA: Electric Power Research Institute; 1986.

37. EPRI Report NP-6045, Evaluation of Flaws in Ferritic Piping. PaloAlto, CA: Electric Power Research Institute; 1988.

38. ASME BPVC Code Case N-463, Evaluation Procedures andAcceptance Criteria for Flaws in Ferritic Piping That Exceed theAcceptance Standards of IWB-3514.2, Section XI, Division 1. In:ASME Boiler and Pressure Vessel Code. New York: American Societyof Mechanical Engineers; 1988.

39. ASME BPVC Section XI, Appendix H, Evaluation of Flaws inFerritic Piping. In: ASME Boiler and Pressure Vessel Code. NewYork: American Society of Mechanical Engineers; 1989.


16 • Chapter 46

40. Scarth DA, et al. Flaw Evaluation Procedures and Acceptance Criteriafor Nuclear Piping in ASME Code Section XI (ASME PVP Vol. 463).New York: American Society of Mechanical Engineers; 2003.

41. ASME BPVC Code Case N-494, Pipe Specific Evaluation Proceduresand Acceptance Criteria for Flaws in Class 1 Ferritic Piping ThatExceed the Acceptance Standards of IWB-3514.2, Section XI,Division 1. In: ASME Boiler and Pressure Vessel Code. New York:American Society of Mechanical Engineers; 1991.

42. Bloom JM, Malik SN. A Procedure for the Assessment of Integrity ofStructures Containing Defects (EPRI Report NP-2431). Palo Alto,CA: Electric Power Research Institute; 1982.

43. Bloom JM. Validation of a Deformation Plasticity Failure AssessmentDiagram Approach to Flaw Evaluation (ASTM Special TechnicalPublication 803). West Conshohocken, PA: American Society forTesting and Materials; 1983: pp. 206–238.

44. Bloom JM. Deformation Plasticity Failure Assessment Diagram. In:Elastic-Plastic Fracture Mechanics Technology (ASTM SpecialTechnical Publication 896). West Conshohocken, PA: AmericanSociety for Testing and Materials; 1985.

45. Bloom JM. Evaluation of Flaws in Ferritic Piping, Appendix J:Deformation Plasticity Failure Assessment Diagram (DPFAD) (EPRIReport NP-7492). Palo Alto, CA: Electric Power Research Institute;1991.

46. Bloom JM. DPFAD for Materials with Non-Ramberg-Osgood Stress-Strain Curves. In: ASME PVP Vol. 287, Fracture MechanicsApplications. New York: American Society of Mechanical Engineers;1994.

47. Bloom JM. Technical Basis for the Extension of ASME Code Case N-494 for Assessment of Austenitic Piping. In: ASME PVP Vol. 304,Fatigue and Fracture Mechanics in Pressure Vessels and Piping. NewYork: American Society of Mechanical Engineers; 1995.

48. Milne I, et al. Background to and Validation of CEGB Report R/H/R6,Revision 3. International Journal of Pressure Vessels and Piping1988;32:105–196.

49. Dowling AR, et al. An Overview of R6 Revision 4. In; ASME PVPVol. 423, Fracture and Fitness. New York: American Society ofMechanical Engineers; 1995.

50. Nilsson F, et al. Elastic-Plastic Fracture Mechanics for Pressure VesselDesign, Research Project 87116, SKI Report TR 89:20; 1989.

51. Andersson P, et al. A Procedure for Safety Assessment of Componentswith Cracks – Handbook, SKI Report 99:49 (Revision 3); 1999.

52. CFR Title 10, Part 50, Appendix G, Fracture ToughnessRequirements. In: Code of Federal Regulations. Washington, DC:National Archives and Records Administration’s (NARA) Office ofthe Federal Register (OFR)/Government Printing Office (GPO); 1983.

53. ASME BPVC Section XI, Appendix G, Fracture Toughness Criteriafor Protection Against Failure. In: ASME Boiler and Pressure VesselCode. New York: American Society of Mechanical Engineers; 1989.

54. U.S. NRC Resolution of the Task A-11 Reactor Vessel MaterialsToughness Safety Issue (NUREG-0744). Washington, DC: U.S.Nuclear Regulatory Commission.

55. ASME BPVC Section XI, Appendix K, Assessment of ReactorVessels With Low Upper Shelf Charpy Impact Energy Levels. In:ASME Boiler and Pressure Vessel Code. New York: American Societyof Mechanical Engineers; 1993: pp. 482.1–482.15.

56. U.S. NRC Regulatory Guide 1.161, Evaluation of Reactor PressureVessels with Charpy Upper-Shelf Energy Less Than 50 ft-lb.Washington, DC: U.S. Nuclear Regulatory Commission; 1995.

57. WRC Bulletin 413, Development of Criteria for Assessment ofReactor Vessels with Low Upper Shelf Fracture Toughness. NewYork: Welding Research Council; 1996.

58. Eason EA, Wright JE, Nelson EE. Multivariable Modeling of PressureVessel and Piping J-R Data (NUREG/CR-5729). Washington, DC:U.S. Nuclear Regulatory Commission; 1991.

59. U.S. NRC Regulatory Guide 1.99, Radiation Embrittlement ofReactor Vessel Materials (Revision 2). Washington, DC: U.S. NuclearRegulatory Commission; 1988.

60. Mehta HS. A Low Upper Shelf Energy Fracture MechanicsEvaluation for a Reactor Pressure Vessel. In: ASME PVP Vol. 260,Fracture Mechanics-Applications and New Materials New York:American Society of Mechanical Engineers; 1993.

61. Griesbach TJ, Smith E. A Review of the ASME Low Upper ShelfEvaluation Procedures for Nuclear Reactor Pressure Vessels. NuclearEngineering and Design 1991;130.

62. Cofie N, Riccardella PC, Yoon K. Technical Basis for Proposed CodeCase N-xxx Alternative Acceptance Criteria and EvaluationProcedure for Flaws in Ferritic Steel Components Operating in theUpper Shelf Range, Revision 4, Presented to Working Group on FlawEvaluation, Orlando, FL, May 10, 2005.

63. Rahman S. Probabilistic Elastic-Plastic Fracture Analysis ofCircumferentially Cracked Pipes with Finite-Length Surface Flaws.Nuclear Engineering and Design 2000;195.


Documents

ASME