ASSESSMENT OF ASME’S FSRF RULES FOR … Section III of the ASME Code, “the fatigue strength ......

ASSESSMENT OF ASME’S FSRF RULES FOR VESSEL AND PIPING WELDS USING A NEW STRUCTURAL STRESS METHOD 31

1 INTRODUCTION

In welded structures, fatigue failures predominantly occurat welded joints. In pressure vessel and piping compo-nents, recent publications, e.g., by Barsom [1] and oth-ers [2], have also pointed out that almost all pressureboundary fatigue failures can be related to welded joints.However, the ASME Boiler and Pressure Vessel Code(Section III and Section VIII) do not explicitly considerthe presence of welded joints. Rather, the design rulesare based on stress (or strain) versus cycles (S-N)fatigue curves generated from smooth base metal spec-imens (i.e., un-welded) more than 30 years ago. For

instance, the Section III fatigue design curves wereobtained by applying a factor of 20 on cycles or 2 onstresses to the mean curves of the best available datafrom smooth base metal specimens. As discussed byBarsom [1], the factor of 20 on cycles was based onengineering judgments to take into account of data scat-ter (a factor of 2), size effect (a factor of 2.5), and sur-face finish as well as atmosphere, etc. (a factor of 4.0).The reduced fatigue strengths for welded joints in Class1 vessels are considered by introducing an appropriatefatigue strength reduction factor (FSRF) comparing withthe smooth specimen S-N design curve [3-4]. Similarly,for Class 1 piping, stress indices are used to account forthe stress concentration effects at welds in calculatingstress intensities in fatigue design and analysis, as dis-cussed recently by Jaske [5] and Hechmer and Kuhn [6].For Class 2 and Class 3 piping, the ASME Code fatigueevaluation methods are based on the Markl’s fatigue

ASSESSMENT OF ASME’S FSRF RULESFOR VESSEL AND PIPING WELDS USINGA NEW STRUCTURAL STRESS METHOD

P. Dong1, J.K. Hong1, D. Osage2, M. Prager3

1Center for Welded Structures Research, Battelle; 2The Equity Engineering Group, Inc.;3Pressure Vessel Research Council (USA)

Corresponding author: [email protected]

ABSTRACT

Fatigue design rules for welds in the ASME Boiler and Pressure Vessel Code are based on the use of FatigueStrength Reduction Factors (FSRF) against a Code-specified fatigue design curve generated from smooth basemetal specimens without the presence of welds. Similarly, Stress Intensification Factors (SIF) that are used in theASME B31 Piping Codes are based on component S-N curves with a reference fatigue strength based on straightpipe girth welds. Typically, the determination of either the FSRF or SIF requires extensive fatigue testing to take intoaccount the stress concentration effects associated with various types of component geometry, weld configuration,and loading conditions. As the fatigue behaviour of welded joints is being better understood, it has been generallyaccepted that the difference in fatigue lives from one type of weld to another is dominated by the difference in stressconcentration. However, general finite element procedures are currently not available for effective determination ofsuch stress concentration effects. This is mainly due to the fact that the stress solutions at a notch (e.g., at weldtoe) are strongly influenced by mesh size at and near a weld, resulting from notch stress singularity. In this paper,a mesh-insensitive structural stress method is used to re-evaluate the S-N test data. Its applications in consistentlyrepresenting the stress concentration effects on fatigue S-N data for pipe girth welds are demonstrated. A single mas-ter S-N approach is presented by means of a mesh-insensitive structural stress parameter formulated within the con-text of fracture mechanics. The major findings are as follows: (a) The mesh-insensitive structural stress method pro-vides a simple and effective mean for characterising stress concentrations at vessel and pipe welds (b) The structuralstress based parameter provides an effective measure of stress intensity at welds, which can be related to fatiguelives. (c) Once the mesh-insensitive structural stress is used, the S-N data processed thus far can be reasonablyconsolidated into one narrow band. Therefore, single master S-N curve for vessel and piping welds can now be estab-lished, regardless of piping weld types or geometries (straight pipe girth welds, different types of flange welds, elbowwelds, mitre bends, etc.), and can be used to general a master fatigue design curve.

IIW-Thesaurus keywords: Fatigue strength; Fatigue tests; Welded joints; Circumferential welds; Pressure vessels;Pipework; Stress; Stress distribution; K1c; Finite element analysis; Fracture mechanics; Structural analysis; Diagrams;Computation; Data; Reference lists.

Welding in the World, Vol. 47, n° 1/2, 2003

IIW-1589-02 (ex-doc. XIII-1929-02/XV-1118-02) recom-mended for publication by Commission XIII “Fatigue ofwelded components and structures”

32 ASSESSMENT OF ASME’S FSRF RULES FOR VESSEL AND PIPING WELDS USING A NEW STRUCTURAL STRESS METHOD

data, in which straight pipe girth weld S-N data wereused as a reference curve with an assigned stress inten-sification factor of unity [7].

As fatigue of welded structures is being better under-stood over the recent years, there has been a growinginterest in improving the fatigue evaluation proceduresfor pressure retaining components [1, 5, 6]. After adetailed review of the ASME pressure vessel and pip-ing fatigue evaluation procedures and the backgrounddocuments, the following areas of concern may be iden-tified for further discussions, technical developments,and improvements.

1.1 Smooth specimens versus welded joints

ASME’s fatigue design curves were based on the datafrom smooth base material specimens in which crackinitiation typically dominates the majority of the fatiguelives. When applying a FSRF for assessing a particularwelded joint in which fatigue life is dominated by prop-agation phenomenon, one assumes that the fatigue livesbetween a smooth specimen and the welded joint canbe scaled by a single parameter FSRF. It is obviousthat the fatigue lives and failure criteria in these two sit-uations differ significantly by definition. That is not saythat the ASME fatigue design rules have not providedfor reliable service. Rather, for lack of the underlyingmechanics in such scaling, most of the specified andempirical-based FSRF tend to give rather high values(as demonstrated later in this paper), resulting in overlyconservative estimation of fatigue life for most applica-tions. Due to their inherent basis, it can be argued thatASME fatigue evaluation procedures can be most con-veniently applied to welded joints that have been groundsmooth.

1.2 FSRF versus stress concentration factors

In Section III of the ASME Code, “the fatigue strengthreduction factor is a stress intensification factor whichaccounts for the effects of a local structural discontinu-ity (stress concentration) on the fatigue strength.” Thisdefinition directly relates FSRF to the conventionalfatigue-notch factor often referred as Kf (the ratio of thefatigue limit for unnotched specimens to that for notchedspecimens). The fatigue notch factor Kf can be esti-mated from elastic stress concentration factor Kt that,however, cannot be easily defined for a typical weldedjoint. Further detailed discussions can be found in [5].Again, such a definition of FSRF works well for relatinginitiation-dominated fatigue lives to notched specimensfrom smooth specimens such as ASME’s average S-Ncurves. However, in dealing with welded joints, in addi-tion to overall stress concentration due to joint geome-try, local discontinuities such as slag inclusions, porosi-ties, and crack-like planar defects can drastically shortenthe initiation part of the fatigue lives, in addition to thepresence of high residual stresses due to welding [8-9].Therefore, the determination of appropriate FSRFs forwelded joints against ASME specified S-N design curvesis no simple matter and mostly done by performing

detailed fatigue testing. Once FSRFs are generated fora given group of weldments, they can only be appliedwithin the confines of similar joint configurations andloading conditions. This is due to the fact that FSRFcannot be viewed as a fundamental based parameter tocorrelate fatigue behavior among different weld geome-tries and loading conditions. Rather, FSRF should beinterpreted as an experimentally determined parameterthat lumps both stress concentration and other welding-related detrimental effects on the reduced fatiguestrength in a welded joint.

1.3 Stress concentration versusfatigue-governing parameter

For welded joints, the difference in stress concentra-tions among different joint types and loading conditionscontributes to the different fatigue behaviors classifiedas weld categories in other industries’ codes and rec-ommended practices such as BS 5500, AWS D1.1, andAASHTO. A series of mostly parallel S-N curves areclassified based on a log-log representation of nominalstress ranges versus cycles to failure, so that both geo-metric and local stress concentrations at welds arealready contained in the S-N data. The existence of thefamily of a series of parallel S-N curves suggests theexistence of a scaling parameter that can be used tocollapse the parallel curves into one single mastercurves within these weld categories, as discussed byBarsom [1], at least for general design and evaluationpurposes. The introduction of an experimentally basedstress intensification factor for a variety of pipe weldconfigurations by Markl in the 1950s [7] should be cred-ited as the first attempt in this regard. In this context, ascaling parameter such as stress intensification factorbecomes more mechanistically plausible in correlatingfatigue behavior from one weld geometry to another incontrast to the use of FSRFs in correlating fatiguestrengths from un-welded smooth bar specimens towelded joints.

As more effective methods become available for char-acterizing stress concentrations at welded joints [9-12],it has now become possible to establish a master weldS-N curve to correlate weld fatigue behaviors in drasti-cally different joint types and loading modes. In thispaper, a brief summary of the finite element basedmesh-insensitive structural stress procedure [9-12] isprovided. The relevant weld fatigue data used by ASMEpressure vessel and piping codes are then re-evaluatedusing the mesh-insensitive structural stress method [11].These include representative data generated by Markl[7, 13, 14] in 1950s, those generated for nuclear pipinglow-cycle fatigue by Heald and Kiss [15], and those morerecently by Scavuzzo et al [16]. Discrepancies as dis-cussed by Scavuzzo et al [16] and Rodabaugh andScavuzzo [17] in correlating SIFs between their dataand those by Markl’s are discussed based on the mesh-insensitive structural stress results obtained for the sameset of fatigue data. Finally, potential improvements tothe ASME’s fatigue evaluation rules are discussed inlight of the present results.


2 MESH-INSENSITIVE STRUCTURALSTRESS PROCEDURE

As reviewed recently by Barsom [1] and Jaske [5]regarding the determination of ASME FSRF for weldedjoints, conventional finite element models cannot bedirectly used to calculate the stress concentration fac-tors due to the inherent stress singularity behavior atweld toe in an idealized finite element model. Instead,hot-spot stress or structural stress extrapolation proce-dures such as those recommended by InternationalInstitute of Welding [18] have been used for some years.Such extrapolation procedures have also been incor-porated in European Pressure Vessel Code [19] forapplications in pressure vessel and piping welds.However, as recently discussed by Dong, et al [10-12],the hot spot stress extrapolation procedures still sufferfrom mesh-size sensitivities in stress determination. Asa result, the hot spot stresses calculated can differ dras-tically if different element sizes at weld toe are used.

With a new definition of structural stress, Dong et al [9]and Dong [10] have developed a robust structural stressprocedure for analyzing welded joints. Its applications infatigue evaluation of welded joints have been given ina series of recent publications [9-12]. In what follows, abrief summary of the mesh-insensitive structural stressprocedure is presented for providing some essentialbackground. Detailed discussions can be found in thecited publications. As discussed by Dong and Dong etal [10-12], a structural stress definition that follows ele-mentary structural mechanics theory can be establishedwith following considerations:

1) It can be postulated that for a given local through-thickness distribution as shown in Fig. 1a obtained from

a finite element model, there exists an equilibrium-equiv-alent structural stress distribution normal to a hypothet-ical cracked plate at a weld, as shown in Fig. 1b, in theform of membrane and bending components. Note thatin fracture mechanics context, such a structural stressdefinition becomes the equivalent far-field stress (σ∞)definition.

2) To ensure mesh-insensitivity, the structural stress σs

calculated must satisfy equilibrium conditions within thecontext of elementary structural mechanics theory atboth the hypothetical crack plane (e.g., at weld toe in Fig.1a) with respect to a reference stress state prescribedby local stresses from typical finite element solutions.The uniqueness of such a structural stress solution canbe argued by considering the fact that the compatibilityconditions of the corresponding finite element solutionsare maintained at this location in such a calculation.

3) While local stresses near a notch are mesh-size sen-sitive due to the asymptotic singularity behavior as anotch position is approached, the imposition of the equi-librium conditions in the context of elementary structuralmechanics within a reference region should eliminateor minimize the mesh-size sensitivity in the structuralstress calculations.

4) Within the context of displacement based finite ele-ment methods, the most accurate solutions are nodaldisplacements and forces at nodal positions, on whichequilibrium conditions are directly enforced. Therefore,the nodal displacements and nodal forces can be directlyused to extract the structural stresses at welds of con-cern, if shell/plate element models are used. As a mat-ter of numerical implementation for solid element mod-els, it can be more convenient to use local stress outputsto calculate equilibrium-equivalent line forces and

Fig. 1. Mesh-size insensitivity in structural stress calculation at weld toe (2D plane-strain model).


moments for extracting the mesh-insensitive structuralstresses.

5) The mesh-insensitivity in calculating structuralstresses at a joint has been demonstrated for variousjoint types in [9-12]. The results on a lap fillet weld areillustrated in Figs. 1-2, where the structural stress at theweld was calculated in the form of equivalent membraneand bending as σs = σm + σb under remote nominalstress (F/A) of unity. The structural stress based stressconcentration at the weld toe is invariant regardless ofelement sizes, element types, either using solid ele-ments or shell element models. Note that in the 3Dmodel representation, a specimen width of 100mm isused in Fig. 2. The difference between 3D solid and 2Dplane strain conditions is solely due to the presence ofedge effects in the 3D shell and solid models, in whichthe high stress concentration is located at the mid-lengthof the fillet weld.

3 MASTER S-N CURVE APPROACH

There exists a large amount of S-N data from a varietyof joint types, weld types, and thicknesses under differ-ent loading conditions (such as remote tension or remotebending). Often, such data are presented in terms ofnominal stress versus cycles to failure (or S-N). A largecollection of such S-N data from the open literature isplotted in S-N format in Fig. 3a. Detailed references andinterpretations will be reported separately [20]. It is worthnoting that the data collection in Fig. 3a reflects the fol-lowing important attributes:

1) Materials: steel yield strength varying from 180MPato 600Mpa.

2) Plate thickness ranging from 2mm to 100mm.

3) Joint types: T-fillet, lap fillet, cruciform joints, longi-tudinal stiffener joints, resistance spot welds, etc.

4) Loading conditions: pure remote tension, pure remotebending, and various mixture in between (e.g., lap shearand lap tension in spot welded coupons).

As expected, the nominal stress based plot in Fig. 3ashows drastically different S-N behaviors among thejoint types and loading modes. Once the mesh-insensi-tive structural stresses were used, Fig. 3b shows that theS-N data band is significantly narrowed. Also note thatthe vertical axis expands only two decades in Fig. 3bversus three decades in Fig. 3a in these log-log plots.A further consolidation requires the consideration of boththickness and remote loading mode effects on the struc-tural stress state at the weld, as discussed in Dong etal [20]. A brief discussion of the master S-N curveapproach is given below.

As discussed by Dong et al [10-12], the mesh-insensi-tive structural stresses can be viewed a stress trans-formation process from complex geometry and loadingconditions to simple structural stress state acting on sim-ple plate. As a result, the stress intensity factor solu-tions for complex geometry and loading conditions canbe calculated with respect to a simple fracture mechan-ics model for which closed form solutions are available.With this approach, a two-stage growth model in theform of a modified Paris Law for crack growth can be for-mulated as [12]:

da= C (Mkn)n (ΔK )m (1)

dN

where m corresponds to the conventional exponent ofParis law. The parameter Mkn is expressed as

Mkn = KNotch (with local notch effects)

(2)Kn (based throught thickness σ t

m and σ tb

Fig. 2. Element-type insensitivity in structural stress calculation at weld toe using 3D modelfor the lap joint shown in Fig. 1.


Fig. 3. Weld S-N data from literature: (a) Nominal stress range versus N,(b) Structural stress range versus N.


The second exponent n in Eq. 1 characterizes the shortcrack growth for a/t < 0.1. The detailed discussions onthe two-stage growth model are given in detail in termsof the mesh-insensitive structural stresses in [11].Fracture mechanics based prediction of life in cycles tofinal failure can be expressed as:

a = a∫

Ν = ∫da

(3)a→0 C (Mkn)n (ΔK )m

where Mkn is dimensionless function of a/t, characteriz-ing notch stress effects at weld, rapidly dying out as a/treaches to about 0.1 [11, 20]. As discussed in [20], theexpression for Mkn requires a structural stress solutionincorporating the self-equilibrating part of the stress stateshown. For simplicity in the present presentation, Mkn

can be ignored in the derivation from this point on with-out losing generality. Detailed Mkn effects can be foundin [20] when initial crack size is considered in Eq. 3.

Note that the integral in Eq. (3) is not sensitive to af,and therefore, can be written as:

N = 1 . tI m

2 . (Δσs)–m I(r ) (4)C

where I(r) is a dimensionless function of r after per-forming the following integration:

a / t = 1

Ι (r) = ∫ d (a / t ) (5)a / t →0 [ƒm (a ) – r (ƒm (a ) – ƒb(a )]mt t t

Eq. 5 can be readily numerically integrated for a givenvalue of initial crack size a/t, as a monotonic function ofthe structural stress bending ratio (r = σb / σs = σb / (σm

+ σb)). If Mkn is not considered, I(r) function is sensitiveto initial crack size a/t in overall magnitude. As initialcrack size varies, a family of parallel I(r) curves can beseen [20]. Due to their self-similar nature, the masterS-N curve approach can be demonstrated by consider-ing one of the curves corresponding an initial crack size

of a/t = 0.001 in Eq. 5 in this paper, as shown in Fig. 4.Eq. 4 can be rewritten as a S-N curve form as follows:

Δσs = C – 1

m . t 2 – m

2m . I (r )1m . N

1m (6)

Eq. (6) uniquely describes a family of structural stressbased S-N curves (Δσs - N)) as a function of the ParisLaw exponent m, thickness effect (t), and bending ratior. From Eq. 6, an equivalent structural stress parame-ter can be formulated as:

ΔSs =Δσs (7)

t 2 – m

2m . I (r )1m

where the thickness term t (2-m)/2m becomes unity for t =1 (unit thickness) and therefore, the thickness t can beinterpreted a ratio of actual thickness t to a unit thick-ness, rendering the term dimensionless. With this inter-pretation, the equivalent ΔSs retains a stress unit.Therefore, Eq. (7) can be directly used to consolidate theS-N data based on the structural stress ranges inFig. 3b. The results are shown in Fig. 5. The effective-ness of the equivalent structural stress parameter givenby Eq. 7 is evident, by comparing with Fig. 3b and Fig. 5.

It should be noted that a similar definition of equivalentstructural stress to Eq. 7 was first used by Maddox [22]in investigating two simple joint types under simple nom-inal tensile stress loading. However, Eq. 7 in terms ofmesh-insensitive structural stresses can be readily gen-eralized for all joint types and loading conditions, as dis-cussed in [11, 20].

Most of the fatigue S-N data in Fig. 3a do not containadequate information regarding actual loading condi-tions (e.g., displacement controlled or load controlled)and associated failure criteria. Therefore, in Fig. 5, dis-placement controlled conditions were assumed in eval-uating I(r) function as shown in Fig. 4. If load controlledconditions are used, an improved consolidation for lowcycle range can be observed. Most of the data

Fig. 4. I(r) functions.


processed so far should fall somewhere in between. InFigs. 4-5, m = 3.6 was based on the crack growth datain carefully controlled notched specimens (without welds)and should be treated as fundamental property on crackgrowth rate, as discussed in [11]. Note that throughoutthis paper, no attempts are made to introduce any empir-ical parameters to achieve a good fit of the data.

Eq. 7 provides a unique representation of a single mas-ter S-N curve in terms of equivalent structural stressranges as a function of Paris law exponent (m), thick-ness (t), loading parameter (r), and implicitly dependenton loading conditions through I(r). Conventional nominalstress based S-N data from various weld types andgeometries can be readily processed once structuralstresses are known, or conversely, the structural stressbased single master curve (ΔSs-N) can be used todeduce the corresponding nominal stress based Δσn -N, simply in the form of:

ΔSs =SCFss

. Δσn (8)

t 2 – m

2m . I (r )1m

In Eq. 8, SCFss refers to the structural stress based SCF,or structural stress calculated at a location of concernat unit load (or F/A = 1) and Δσn refers to the conven-tional nominal stress definition (e.g, F/A).

4 PRESSURE VESSELAND PIPING WELDS

Having provided some background regarding the mesh-insensitive structural stress procedures and relevant for-mulations for the effective structural stress parameterΔSs in defining the single master S-N curve, we nowmove on to re-evaluate the weld S-N data relevant toASME’s FSRF rules using the methodologies discussedin the previous sections. We will start with the mostrecent pipe girth weld data by Scavuzzo et al [16], sincetheir report provided detailed documentation of the rawtest data.

4.1 Data from Scavuzzo et al.

As shown in Fig. 6, four-point bending fatigue tests wereperformed recently by Scavuzzo, et al [16] on both car-bon steel pipes (ASTM A53 Type F) and stainless steelpipes (ASTM A312 Type 304). Two pipe wall thicknesswere used, 0.2” and 0.237”. The tests were performedto address the applicability of stress intensification fac-tor i = 1 for pipe wall thickness less than 0.237” and toextend the FSRF data base for pipe girth welds into the“low-cycle” range (100 to 2000). However, the tests by

Fig. 5. Equivalent Structural Stress Range versus N for all S-N data in Fig. 3.

Fig. 6. Four-Point Bending Fatigue Test on Girth Welded Pipe by Scavuzzo et al [16].


Scavuzzo et al [16] generated the unexpected lowerstress intensification factor (e.g., i ≈ 0.28 for 285 cyclesto failure) than that (i.e., i ≈ 1) for similar pipe welds rec-ommended by Markl [5].

With the mesh-insensitive structural stress proceduresdiscussed earlier, 3D solid element models were usedto simulate the four-point bending conditions depicted inFig. 6. The structural stress based SCF adjacent to weldtoe are calculated as SCF = 1.04 for wall thickness of0.237” and SCF ≈ 1. for wall thickness of 0.2”. The dif-ference in the structural stress based SCFs betweenthe two pipe thicknesses is insignificant. The low struc-tural stress based SCFs for the girth weld and loadingconditions are as expected, since the structural stressescan be interpreted as generalized nominal stressesunder complex loading. Under statically determinateloading conditions and with a clearly defined nominalstress state, such as the cases of the girth-weldedstraight pipes depicted in Fig. 6, the structural stresscalculated approaches the nominal stress.

4.2 Data from Heald and Kiss

Heald and Kiss reported a series of low-cycle fatiguedata for welded nuclear piping (carbon steel and stain-less) in 1974 [15]. The piping specimens reportedinclude “butt-welded pipes”, elbows, and tees, testedunder cantilever-bending conditions. However, detailedspecimen geometry and weld configurations needed forthe current structural stress based analysis were notreported in their paper. Instead, we had to rely on theinterpretations given by Rodabaugh and Scavuzzoreported in [17]. As reported in [17], “butt-welded pipes”referred in Heald and Kiss [15] in all likelihood were ofthe “welding neck flange” as used by Markl [7] and Markland George [13]. The flange butt-welded girth weld isdepicted in Fig. 7, taken directly from [17]. If this was thecase, the structural stress based SCF of 1.36 at theweld toe was calculated in this investigation on theflange side for pipe wall thickness of 0.28” for the testsperformed by Heald and Kiss [15].

It is important to note that Markl [7] did not provide aspecific definition of “straight pipe girth welds”. As men-tioned earlier, Rodabaugh and Scavuzzo [17], aftercross-comparing a series of Markl’s publications, con-cluded that Markl’s “straight pipe girth welds” more orless represent the “welding neck flange” attached to astraight pipe with a girth weld, not the actual straightpipe girth welds tested by Scavuzzo et al [16]. In thelatter, the structural stress based SCF is significantlylower, merely 1.04 for the actual pipe girth welds testedin [16] than that for the “welding neck flange” joints. Forthe “welding neck flange” joints tested by Markl [7] andthe “straight pipe girth welds” tested by Heald and Kiss[15], the structural stress based SCF ranges from 1.35-1.4 under cantilever-bending conditions, depending onthe actual pipe wall thickness. This, in part, can explainthe elevated S-N curve (in terms of nominal stress) gen-erated by Scavuzzo et al [16] due to the low SCF intheir specimens, rather than low-cycle fatigue phenom-enon as discussed in [16]. At this point, it should bepointed out that Markl’s stress intensification factor i =1 for “straight pipe girth welds” (his baseline weld S-Ncurve) should be i ≈ 1.36 or thereabout, actually repre-senting “welding neck flange” girth weld to a straightpipe.

4.3 Data from Markl, Markl and George

Markl [7] reported a comprehensive S-N data set forpipe welds ranging from “straight pipe girth welds”, toflange assemblies, to welded bend connections. Heintroduced the stress intensification factor (i) as a sin-gle parameter to correlate the S-N curves generated fordifferent pipe weld configurations. The stress intensifi-cation factor in this context serves as an experimentalbased measurement of the stress concentration effectson fatigue strength. However, it is rather unfortunatethat the baseline case (i = 1) was not clearly established,without clearly defining the “straight pipe girth welds”.The same sentiment was shared by Rodabaugh andScavuzzo [17]. Without being able to find the detailedgeometry definition for Markl’s “straight pipe girth welds”,

Fig. 7. Cantilever Testing for “Butt Girth Weds” Using by Markl [7] and Markl and George [13]with Lc = 47», and Heald & Kiss [15] with Lc = 237», based on interpretations by Rodabaugh

and Scavuzzo et al [17].


the interpretations given by Rodabaugh and Scavuzzo[17], as shown in Fig. 7, were used for performing thestructural stress analysis in this investigation. For a nom-inal pipe size of 4.5” OD and wall thickness of 0.237, theSCF becomes 1.37, assuming that the girth weld waslocated right at the tapered flange end in Fig. 7 (thisseems to be the case in view of Fig. 5 of [13]).

Weld S-N data from various welded pipe bends (elbows,tees, and mitre bends, etc.) were reported by Markl [7,14]. One major difficulty in interpreting this set of S-Ndata under either in-plane or out-of-plane bending is thatMarkl [7,14] did not provide the actual test load or dis-placement at loading position. Instead, Markl [7,14]reported his data based on nominal stresses. For mostof the specimens and loading modes, nominal stressescannot be consistently defined and calculated withrespect to the failure locations reported in [7,14].

As an example, as shown in Fig. 8 for welded mitrebends reported by Markl [14], the critical location basedon the present structural stress methods under out-of-plane bending (unit load Fz) is identified at Location Ashown in Fig. 8. The direction of the structural stress isnormal to the weld line. However, the authors are notaware of any nominal stress formulation for this case.The “nominal stress” used for this case by Markl [14] isbased on Mises stress or equivalent stress in terms of“bending stress (Sb2) transverse to the plane of curva-ture and torsional stress (St)” as:

S’n2 = √S 2b2 + 3 . S 2

t (9)

The section modulus was calculated based on thestraight pipe [7]. Two issues become apparent. In Eq.9 by Markl [14], both of the stress components cannotbe calculated with any reasonable degree of accuracyfrom elementary theory for the mitre bend under thegiven loading mode. Even if they can be calculated, Eq.9 can only serve as a nominal equivalent stress defini-tion, rather nominal stresses that can be linearly relatedto the load level.

Since actual applied load level for each of the S-N datapoints was not reported in [7,14], S’n2 in Eq. 9 has to beused to infer the corresponding load level for the struc-tural stress calculation in this investigation. For a givenS’n2 it is assumed that Sb2 is the nominal bendingstresses normal to the weld line and St can beexpressed with the projected torsional moment onto theplane described by the circumference of the weld. Inthis way, Sb2 calculated can be scaled by the structuralstresses calculated at Position A under unit load at theloading point shown in Fig. 8. It should be noted that theerror in using the sectional modulus from the pipeinstead of the weld cross-section can be significant bothin the present calculations (due to lack of information)and in [7, 14].

To gain confidence in the structural stress based inter-pretation of the pipe weld S-N data, a further search oftest data on mitre bends unveiled those by Macfarlane[21] in 1962. The welded mitre bend pipes tested byMacfarlane [21] are geometrically similar to those byMarkl [14]. However, Macfarlane used a loading mech-anism that provided a pure bending action within themiddle section of the bend for both in-plane and out-of-plane loading mode. In addition, the loading levels (con-stant magnitude loading) were documented for eachdata point. The data for the similar mitre bend configu-rations to the one shown in Fig. 8 are processed usingthe mesh-insensitive structural stress method. Theseinclude in-plane bending, out-of-plane bending, andpressure pulsation.

5 S-N DATA INTERPRETATIONAND DISCUSSIONS

The nominal stress range based plot of the pipe weld S-N data are summarized in Fig. 9a. Some plate weld S-N data from [10-12] (included in Figs. 3 and 5 of thispaper) are also included for comparison purposes in

Fig. 8. Mitre-Bend Pipe Weld Fatigue Tests by Markl [7, 14].


Fig. 9. The solid symbols signify the pipe weld datadirectly relevant to ASME fatigue design rules, while theempty symbols represent the plate weld data collectedfrom wide range joint types and loading modes. Asexpected, the S-N data showed a wide scatter, particu-larly from Markl’s data. Based on the structural stressescalculated in this investigation as discussed in the pre-vious section, Fig. 9b summarizes the same set of theS-N data in Fig. 9a, but using structural stress ranges.All the S-N data points essentially fall into a narrow bandin Fig. 9b from N = 102 up to N = 107. Fig. 10 shows theresults if the equivalent structural stress range (ΔSs) isused with m = 3.6, as in Fig. 5, by assuming either dis-

placement controlled testing conditions (Fig. 10a) or loadcontrolled conditions (Fig. 10b). An improved consoli-dation of the S-N can be seen, although the differencebetween Fig. 9a and Fig. 10 is not as significant as thatbetween Fig. 3b and Fig. 5. But, the effectiveness ofusing ΔSs is clearly seen in Fig. 5 for more drasticallydifferent joint types, thickness, and loading conditionsthan those considered in Fig. 10. Note that detailed load-ing conditions cannot be found for more than half of theS-N data shown in Fig. 9a. The actual conditions couldmostly likely be situated in between, depending on fail-ure criteria and how loads are monitored and main-tained.

Fig. 9. ASME code related pipe weld S-N data (solid symbols) and plate weld S-N data (empty symbols):(a) Nominal stress range versus N; (b) Structural stress range versus N.


For practical applications, the trend line of the narrowband of S-N data in Fig. 10a, or Fig. 10b can be usedto establish a master S-N curve for the joint types ana-lyzed. The consolidation of the wide range of S-N datain terms of nominal stresses is accomplished by incor-porating the stress concentration effects captured in themesh-insensitive structural stresses (Fig. 9b), and thick-ness effects (t (2-m)/2m), and loading mode parameter I(r)in Eq. 7. As illustrated in Fig. 10, once the structuralstress parameter is known, the empirical based stressintensification factors or FSRSs are no longer neededin performing fatigue evaluations or interpreting test data.If the variations in both thickness and loading mode arenot significant, the structural stress Δσs can be nearly as

effective as the equivalent structural stress ΔSs, com-paring Figs. 9b and Fig. 10. It is important to note thatthe introduction of the stress intensification factor byMarkl [7] was intended to achieve the same objective,but without providing consistent and adequate analyti-cal means in doing so at that time.

In contrast, the FSRF definition in ASME code can onlybe viewed as an empirical parameter since the baselinereference mean fatigue curve from smooth specimenscannot be related to weld fatigue curves with any knownmechanics basis. Although the ASME design curveshave provided reliable fatigue designs over the years,their success, to a large extent, can be attributed their

Fig. 10. ASME code related pipe weld S-N data (solid symbols) and plate weld S-N data (empty symbols)using the equivalent structural stress range ΔSs (Eq. 7 with m = 3.6).


excessive conservatisms in specifying very high valuesof FSRF. For instance, as discussed by Jaske [5], anozzle fillet weld has a FSRF of about 4.0 in ASMEVessel Code. If the definition FSRF can be directlyrelated to global stress concentration effects (withoutdetailed local weld profile variation effects), a globalstress concentration factor of 4.0 even within linear elas-tic context cannot be reached. With the mesh-insensi-tive structural stress method, almost all available weldS-N data published data over the last 25 years havebeen processed at Battelle. Thus far, the structuralstress based SCFs rarely reach to 2.0, except for somejoints with partial thickness failure definition, circular plugwelds, and resistance spot welds.

Two factors may have contributed to the excessivelyhigh FSRF values in the ASME code: one is the refer-ence mean S-N curve from the smooth specimens(superimposed in Fig. 9a); the other is that the largedata scatter such as that shown in Fig. 9a when “nom-inal stresses” are used, often without a clear definitionsuch as that in Eq. 9 for welded pipe bends. Forinstance, to scale the S-N data corresponding to themitre bends from Markl [7, 14] and Macfarlane [21]shown in Fig. 9a against the ASME mean curve, anextremely high value of FSRF or SIF has to be intro-duced. In Fig. 9b, the structural stress range versuscycle to failure plot indicates that the stress concentra-tion effects captured in the structural stress definitionare able to consolidate the data reasonably well. Any fur-ther differences in the S-N behaviors shown in Fig. 9b,in addition to typical scatter band inherent within thesame joint types and test conditions, can be attributedto the difference in loading modes, thickness variations,as well as materials. Those effects can be adequatelytaken into account in Eqs. 6-7 in the form of a masterS-N curve for typical welded joints, if propagation dom-inates the fatigue lives. As such, the conventional defi-nition of FSRF or SIF (i) for any specific joint type andloading mode is fully captured. If FSRF or SIF (i) needsto be recovered for a joint type of interest, in which nom-inal stress Δσn can be defined, Eq. 8 provides a simpleexpression as follows:

FSRFss =SCFss (10)

t 2 – m

2m . I (r )1m

where, FSRFss signifies the fact that the fatigue strengthreduction factor is based on the structural stress defin-ition. As shown in Fig. 4, I(r) is essentially constant overbending ratio r = 0 to 1 under load controlled conditions.Then, FSRFss is solely determined by SCFss and thick-ness at a location of interest. Further more, for jointswithin a similar thickness range, FSRFss = SCFss may beused, as shown in Fig. 9b.

Further detailed results by considering the self-equili-brating part of the stress distribution will be reported in[20], where the consideration of the detailed effects ofMkn (Eq. 3) on the I(r) function will be discussed.However, for general design rules and potential codeapplications, the approach presented in this paper iseasier to implement in practice.

6 SUMMARY

In this paper, a mesh-insensitive structural stress pro-cedure is presented. Its applications in consistently rep-resenting the stress concentration effects on fatigue S-N data for pipe girth welds are demonstrated. A singlemaster S-N approach is presented by means of a mesh-insensitive structural stress parameter formulated withinthe context of fracture mechanics. The following obser-vations can be made:

1) The ASME fatigue strength reduction factor (FSRF)or stress intensification factor (i) was introduced morethan 30 years ago to correlate S-N fatigue data fromwelded joints to the data obtained from small smoothbar specimens. Due to the lack of underlying mechan-ics in such correlations, the definition of FSRF or i wasbased on empirical observations and can only bededuced from fatigue testing of various joint types. Asa result, its applications are strictly limited within theconfines of these tests.

2) The mesh-insensitive structural stress method pro-vides a robust calculation procedure for capturing thestress concentration effects on fatigue behavior of weldedjoints. Its effectiveness is demonstrated by not only con-solidating the pipe weld S-N data relevant to ASMEcodes, but also consolidating the pipe data with platejoint data collected from drastically different thicknesses,loading modes, and joint configurations. This suggeststhe existence of a master S-N curve for weld joints, atleast for general design and evaluation purposes.

3) Once such a master curve is established with rep-resentative S-N from selected fatigue testing in con-trolled environment, the structural stress based fatigueparameter ΔSs can be used to relate the master ΔSs-Ncurve to the conventional nominal stress based S-Ndata. As a result, the structural stress based FSRF or ican be analytically determined after structural stress cal-culations. Ambiguities and arbitrariness often encoun-tered in code applications can be avoided in deciding anappropriate FSRF or i. Costly fatigue testing for extract-ing these factors can be minimized, if not eliminated.Fatigue life estimation for actual structures under real-istic loading conditions can be carried out by simplyrelating structural stresses calculated to the master ΔSs-N curve. For variable amplitude loading, conventionalcycle counting methods and Miner s rule summation ofdamage can be applied as usual.

REFERENCES

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2. ASME Section XI Task Group on Fatigue OperatingPlants, “Metal Fatigue in Operating Nuclear Power Plants”,Welding Research Council Bulletin 376, November 1992.

3. ASME Criteria of the ASME Boiler and Pressure VesselCode for Design by Analysis in Sections III and VIII, Division2, American Society of Mechanical Engineers, 1969.


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9. Dong, P., Zhang, J., and Hong, J.K., “Structural StressAnalysis Procedures”, US and International PatentApplications, November 2000.

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11. Dong, P., Hong, J.K., and Cao, Z., “A Mesh-InsensitiveStructural Stress Procedure for Fatigue Evaluation ofWelded Structures”, International Institute of Welding, IIWDoc. XIII-1902-01/XV-1089-01, July 2001.

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13. Markl, A.R.C. and George, H.H., “Fatigue Tests onFlanged Assemblies”, Trans. ASME, Vol. 72, pp. 77-87,1950.

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17. Rodabaugh, E.C. and Scavuzzo, R.J., “Effect of TestingMethods on Stress Intensification Factors”, Report 2 inFatigue of Butt-Welded Pipe and Effect of Testing Methods,Welding Research Council Bulletin 433, July 1998.

18. “Stress Determination for Fatigue Analysis of WeldedComponents”, IIS/IIW 1221-93, Abington Publishing,Abington Cambridge, 1993.

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ASSESSMENT OF ASME’S FSRF RULES FOR … Section III of the ASME Code, “the fatigue strength ......

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