Proceedings of the ASME 2017 Pressure Vessels and Piping ConferencePVP2017

July 16-20, 2017, Waikoloa, Hawaii, United States

PVP2017-66271

CONSIDERATION OF REDUCTION IN STIFFNESS DUE TO CRACKING AND THEIMPACT ON STANDARD STRESS INTENSITY FACTOR SOLUTIONS

Daniel M. BlanksQuest Integrity Group

Gold Coast, Queensland, AustraliaEmail: d.blanks@questintegrity.com

ABSTRACTAn API 579-1/ASME FFS-1 Failure Assessment Diagram

based Fitness-for-Service assessment was carried out on an em-bedded crack-like flaw found in a nozzle to shell weld in a pres-sure vessel. Stress intensity factors were initially calculated byutilizing stress results from a Finite Element Analysis (FEA) ofan uncracked configuration, with the standard embedded crackstress intensity factor solution given in API 579-1/ASME FFS-1.Due to the complex nozzle geometry and flaw size, a second anal-ysis was carried out, incorporating a crack into the FEA model,to calculate the stress intensity factors and evaluate if the stan-dard solution could be applied to this geometry.

A large difference in the resulting stress intensity factors wasobserved, with those calculated by the FEA with the crack incor-porated into the model to be twice as high as those calculated bythe standard solutions, indicating the standard embedded crackstress intensity factor solution may be non-conservative in thiscase. An investigation was carried out involving a number ofstudies to determine the cause of the difference. Beginning withan elliptical shaped embedded crack in a plate, the stress inten-sity factor calculated with an idealized 3D crack mesh agreedwith the API 579-1/ASME FFS-1 solution. Examining othercrack locations, and crack shapes, such as a constant depth em-bedded crack, revealed how the solution began to differ.

The greatest difference was found when considering a crackmesh with a small component height (i.e. the distance measuredperpendicular from the crack face to the top of the mesh). Aclose agreement was then found between the stress intensity fac-tors calculated in the nozzle model and an idealized crack meshwith component heights representative of the true geometry. This

revealed that reduced structural stiffness is a key factor in thecalculation of the stress intensity factors for this geometry, dueto the close proximity of the embedded crack to the inner sur-face of the nozzle. It was found that this reduction is potentiallysignificant even with relatively small crack sizes.

This paper details the investigation, and aims to provide thereader with an awareness of situations when the standard stressintensity factor solutions may no longer be valid, and offers gen-eral recommendations to consider when calculating stress inten-sity factors in these situations.

NOMENCLATURE2a full depth of crack.2c full length of crack.σbe bending stress.σme membrane stress.σyy stress normal to the crack.ϕ elliptic angle around crack front.d size of ligament.d1 distance from plate internal surface to centre of crack.d2 distance from plate external surface to centre of crack.FEA Finite Element Analysis.K1 Mode I stress intensity factor.L component height.L1 distance from crack plane to bottom of component.L1 distance from crack plane to top of component.t thickness of component.W distance from centre of crack to free edge.x local coordinate originating at the internal surface.

1 Copyright c© 2017 by ASME

INTRODUCTIONAn API 579-1/ASME FFS-1 [1] Failure Assessment Dia-

gram based Fitness-for-Service assessment was carried out on acrack-like flaw found in a nozzle to shell weld of a pressure ves-sel. The nozzle geometry and location of the crack-like flaw canbe seen in Fig. 1, with dimensions shown in Fig. 2. The nozzleis loaded under internal pressure and dead weight.

Initially the stress intensity factors were calculated by utiliz-ing the results from a stress analysis of the uncracked configu-ration, with the standard stress intensity factor solution given inAPI 579-1/ASME FFS-1. Due to the complex geometry and flawsize, a second analysis was carried out, incorporating a crack-like flaw directly into the stress analysis, to calculate the stressintensity factor and to evaluate the applicability of the standardsolution.

FIGURE 1: CRACK-LIKE FLAW IDENTIFIED IN THE NOZ-ZLE TO SHELL WELD.

CALCULATION OF STRESS INTENSITY FACTORS US-ING A STANDARD SOLUTION

The crack-like flaw was idealized as an embedded crack ofelliptical shape in a plate. From the results of an ultrasonic in-spection, the flaw sizing was taken to be 30mm deep, 80mmlong, and with a 5mm remaining ligament to the ID surface ofthe vessel. The thickness of the component at the location ofthe flaw was 40.4mm. The distance from the centre of the crackto the free edge was 250mm wide, taken as half the nozzle cir-cumference. The flaw sizing is summarized in Tab. 1, using thegeometry convention shown in Fig. 3.

A stress analysis of the uncracked configuration was carriedout using a Finite Element Analysis (FEA). Abaqus/CAE and

FIGURE 2: COMPONENT DIMENSIONS.

TABLE 1: CRACK-LIKE FLAW DIMENSIONS.

Dimension Value [mm]

Full depth of embedded crack, 2a 30

Full length of embedded crack, 2c 80

Distance from plate surface to centre ofembedded crack, d1

20

Thickness of component, t 40.4

Distance from centre of crack to free edge, W 250

Size of ligament, d (d = d1 −a) 5

FIGURE 3: EMBEDDED ELLIPTICAL CRACK IN A PLATEGEOMETRY [1].

Abaqus/Standard [2] were used to create and solve the 3D finiteelement model respectively.

The stress distribution, σyy was extracted at the location ofthe highest stress at the crack, in the direction normal to the plane

2 Copyright c© 2017 by ASME

FIGURE 4: STRESS DISTRIBUTION NORMAL TO CRACKPLANE [MPa] AT THE LOCATION OF THE CRACK IN THEUNCRACKED CONFIGURATION STRESS ANALYSIS.

0 0.2 0.4 0.6 0.8 10

20

40

Normalized distance through thickness, x/t

Stre

ssno

rmal

tocr

ack,

σyy[M

Pa]

Actual stress distributionLinearized stress distribution

FIGURE 5: UNCRACKED STRESS DISTRIBUTION AT THECRACK.

of the crack, along a path in the through-wall direction. This lo-cation, and the path used for stress extraction, is shown in Fig. 4.The statically equivalent membrane and bending components ofthe stress distribution were calculated [1], to give the linear stressdistribution to be used in the stress intensity factor solution. Fig-ure 5 plots the stress distribution normal to the crack plane alongthe path, along with the linearized distribution. Whilst the lin-earized distribution does not capture the peak stresses at x/t = 0and x/t = 1, these stresses are artificial due to sharp corners inthe mesh at these locations, and so their omission from the lin-earization is of no concern. The resulting membrane and bendingcomponents are summarized in Tab. 2.

The stress intensity factor for a plate with an embeddedcrack, of elliptical shape, with a through-wall membrane andbending stress, was used for this assessment (solution numberKPECE1 in API 579-1/ASME FFS-1).

TABLE 2: LINEAR STRESS DISTRIBUTION.

Stress Component Value [MPa]

Membrane stress, σme 13.2

Bending stress, σbe 11.0

FIGURE 6: QUARTER SYMMETRIC CRACK MESH OF ANEMBEDDED ELLIPTICAL CRACK IN A PLATE.

This solution has a number of crack and geometry dimen-sional limits. One of the limits requires d/t to be greater than 0.2,however for this geometry d/t = 0.12. As the crack is outsideof the limits, the standard solution may no longer be accurate,so to evaluate the accuracy of the solution, a FEA of a quartersymmetric crack mesh of the same geometry (embedded ellipti-cal flaw in a plate) was carried out. The 3D finite element crackmesh was created using the automatic mesh generation softwareFEACrack [3], and solved using the in-built solver Warp3D [4].The crack mesh was loaded using the membrane and bendingstresses as per Tab. 2. The crack mesh and relevant dimensionscan be seen in Fig. 6.

The resulting stress intensity factors, KI , calculated by thestandard solution KPECE1 and the embedded elliptical crackmesh are plotted around the crack front in Fig 7. As can be seen,very close agreement is shown between the two methods, indi-cating that whilst the crack is outside the geometry dimensionallimits, the standard solution was still applicable.

CALCULATION OF STRESS INTENSITY FACTORS US-ING A CRACKED MODEL

A crack mesh was inserted into the global mesh of the pres-sure vessel, as seen in Fig. 8. To more closely replicate the crack-like flaw as measured, the crack was modelled as a constant depthembedded flaw, with dimensions as per Tab. 1. The crack frontand relevant dimensions can be seen in Fig 9. Abaqus/CAE and

3 Copyright c© 2017 by ASME

90 135 180 225 270

60

80

100

120

Elliptic angle around crack front, ϕ [◦]

Stre

ssIn

tens

ityFa

ctor

,KI[ N

mm

−1.

5]

KPECE1Embedded ellipticalcrack mesh

FIGURE 7: COMPARISON OF KI AROUND THE CRACKFRONT FOR THE STANDARD SOLUTION KPECE1 ANDAN EMBEDDED ELLIPTICAL CRACK IN A PLATE.

FIGURE 8: CRACK MESH INCORPORATED INTO THEVESSEL MODEL. GLOBAL MESH SHOWN IN RED,CRACK MESH SHOWN IN GREEN. HALF SECTION OFMODEL SHOWN FOR CLARITY.

Abaqus/Standard were used to create and solve the combined 3Dfinite element model respectively.

A plot of the von Mises (equivalent) stress at the crack isshown in Fig. 10. The resulting stress intensity factor calcu-lated from the model is compared against the KPECE1 solutionin Fig. 11. The elliptic angle convention is as per Fig. 3, whereϕ = 90◦ is at the crack front closest to the OD, and ϕ = 270◦ isat the crack front closest to the ID.

As can be seen, there is a large difference between the tworesults, especially at the 90◦ and 270◦ points, where the crack ex-tension direction is towards the OD and ID respectively. When

FIGURE 9: DIMENSIONS OF CRACK INCORPORATEDINTO THE VESSEL MODEL. CRACK FRONT SHOWN INBRIGHT RED. NOZZLE NECK REMOVED FOR CLARITY.

FIGURE 10: VON MISES STRESS DISTRIBUTION [MPa] ATTHE CRACK INCORPORATED INTO THE MODEL. HALFSECTION OF MODEL SHOWN FOR CLARITY. DEFORMA-TION SCALE 500×.

compared to the KPECE1 solution, the stress intensity factor cal-culated for the crack incorporated into the model is 2.2× greaterat the 90◦ point (70Nmm−1.5 vs. 153Nmm−1.5), and 1.8×greater at the 270◦ point (129Nmm−1.5 vs. 229Nmm−1.5).

INVESTIGATIONTo understand the cause of the difference, an investigation

was carried out involving three studies, trialling different ideal-ized geometries. The first was a comparison between the stressintensity factor calculated for an embedded elliptical crack (i.e.KPECE1) and an embedded constant depth crack (as used in thecracked model). The second study investigated the sensitivity ofthe component height L (refer to Fig. 6) to the calculation of thestress intensity factor, as in the cracked model this dimension onone side of the crack is relatively small. The third study explored

4 Copyright c© 2017 by ASME

0 90 180 270 3600

50

100

150

200

250

Elliptic angle around crack front, ϕ [◦]

Stre

ssIn

tens

ityFa

ctor

,KI[ N

mm

−1.

5]

Cracked vessel modelKPECE1

FIGURE 11: COMPARISON OF KI AROUND THE CRACKFRONT FOR THE CRACK INCORPORATED INTO THEVESSEL MODEL AND THE STANDARD SOLUTIONKPECE1.

FIGURE 12: QUARTER SYMMETRIC CRACK MESH OF ANEMBEDDED CONSTANT DEPTH CRACK IN A PLATE.

the sensitivity of the crack size on the calculation of the stressintensity factor when comparing the crack mesh and standard so-lution methods.

Study into Embedded Elliptical Crack vs EmbeddedConstant Depth Crack Stress Intensity Factors

A quarter symmetric crack mesh of a plate with an embed-ded constant depth crack was created, to compare with the em-bedded elliptical crack used previously. All dimensions and load-ings were kept identical, and only the crack shape was changed.The crack mesh can be seen in Fig. 12.

The resulting stress intensity factors calculated by bothmeshes are plotted around the crack front in Fig. 13.

90 135 180 225 2700

50

100

150

Elliptic angle around crack front, ϕ [◦]

Stre

ssIn

tens

ityFa

ctor

,KI[ N

mm

−1.

5]

Embedded ellipticalcrack meshEmbedded constantdepth crack mesh

FIGURE 13: COMPARISON OF KI AROUND THE CRACKFRONT FOR AN ELLIPTICAL SHAPED EMBEDDEDCRACK AND A CONSTANT DEPTH EMBEDDED CRACK.

For the constant depth crack, at the 90◦ and 270◦ pointsthe stress intensity factor was calculated to be 80Nmm−1.5 and144Nmm−1.5 respectively. As expected, due to the reduced ef-fective ligament, the constant depth crack had a slightly higherstress intensity factor, with an increase of 10 to 15%. This is,however, still well below the stress intensity factor calculated bythe crack incorporated into the model.

Study into the Sensitivity of the Component Height onthe Stress Intensity Factor

The standard stress intensity factor solutions are applicableunder the assumption that the geometry of the crack does not re-sult in a significant loss of stiffness in the component [1]. Reduc-ing the component height, L, will result in a loss of stiffness, andso the sensitivity into this dimension was studied with a numberof different meshes. Six quarter symmetric crack meshes werecreated, for an embedded constant depth crack in a plate withdifferent L dimensions (1000, 500, 100, 50, 20 and 10mm). Allother dimensions remained constant. The loading (as per Tab. 2)was applied as an equivalent crack face traction [5].

The resulting stress intensity factors calculated for each ge-ometry case are summarized at key points on the crack front inTab. 3.

As can be seen, when the component height reduces thestress intensity factors significantly increase. At the componentheight of 10mm, the stress intensity factor is more than 2.3×greater than that calculated at a component height of 500mmand 1000mm, where the solution has converged. This highlightsthe large effect on the stress intensity factor calculation that areduction in stiffness due to cracking can have.

5 Copyright c© 2017 by ASME

TABLE 3: COMPARISON OF KI AT KEY POINTS ONTHE CRACK FRONT FOR A RANGE OF COMPONENTHEIGHTS FOR AN EMBEDDED CONSTANT DEPTHCRACK IN A PLATE.

Component Height, L[mm]

Stress Intensity Factor, KI[Nmm−1.5] at crack front angles, ϕ

0◦/180◦ 90◦ 270◦

1000 55.7 80.1 144.0

500 55.7 80.1 144.0

100 58.2 84.0 148.1

50 61.8 93.3 158.5

20 71.5 124.6 193.7

10 123.3 252.1 335.3

For the crack incorporated in the model, the stress intensityfactor at 270◦ is 229Nmm−1.5. Comparing this to the embed-ded constant depth crack in a plate with a component height of10mm, which is close to the distance between the crack face andthe nozzle pipe ID, the stress intensity factor at 270◦ is nearly50% higher, at 335Nmm−1.5.

This discrepancy is due to the idealized plate model havinga symmetric component height, L, (i.e. the same L on both sidesof the crack), whilst the crack incorporated in the model has anon-symmetric component height, with L1 = 11mm towards thenozzle pipe ID, and L2 = 71mm to the edge of the compensationpad (refer to Fig. 2).

To account for this in the plate crack model, another meshwas created, using half symmetry and positioning the crack11mm from the top of a plate 82mm long. The loading (as perTab. 2) was applied as an equivalent crack face traction. Thismesh can be seen in Fig. 14.

The resulting stress intensity factors calculated from thehalf symmetric plate mesh are compared against those calculatedfrom the crack incorporated into the model in Fig. 15.

As can be seen, the stress intensity factors are in very goodagreement at the 90◦ and 270◦ positions around the crack front.The stress intensity factors differ around the 0◦ and 180◦ posi-tions, which is a result of the stress distribution applied to theplate model. This distribution was taken from the uncrackedmodel where the stresses were highest, which was at the 90◦ /270◦ position. At the 0◦ and 180◦ positions the stress profilediffers, resulting in a different stress intensity factor being calcu-lated for the crack incorporated into the model.

FIGURE 14: HALF SYMMETRIC CRACK MESH OF AN EM-BEDDED CONSTANT DEPTH CRACK WITH L1 = 11mmAND L2 = 71mm.

0 90 180 270 3600

50

100

150

200

250

Elliptic angle around crack front, ϕ [◦]

Stre

ssIn

tens

ityFa

ctor

,KI[ N

mm

−1.

5] Half symmetric crackmeshCracked vessel model

FIGURE 15: COMPARISON OF KI AROUND THE CRACKFRONT FOR A CONSTANT DEPTH EMBEDDED CRACK INA HALF SYMMETRIC PLATE AND THE CRACK INCOR-PORATED INTO THE VESSEL MODEL.

Study into the Sensitivity of the Crack Size on theStress Intensity Factors

The size of the crack also has an effect on the stiffness of thecomponent. To investigate the sensitivity of the crack size whenconsidering a reduced component height, stress intensity factorswere calculated for a number of crack sizes using the crack meshapproach, and compared against the standard solutions. Six half

6 Copyright c© 2017 by ASME

TABLE 4: COMPARISON OF KI AT ϕ = 270◦ CALCULATEDUSING A CRACK MESH AND THE STANDARD SOLUTIONFOR A RANGE OF CRACK SIZES FOR AN EMBEDDED EL-LIPTICAL CRACK IN A PLATE.

Crack depth, 2a[mm]

Stress Intensity Factor, KI [Nmm−1.5]at ϕ = 270◦

Crack mesh KPECE1

30 206.5 129.4

25 153.8 103.9

20 113.8 84.2

15 82.3 67.4

10 56.8 51.4

5 35.1 34.2

symmetric crack meshes were created, with non-symmetric com-ponent heights as used previously (refer to Fig. 14). To enablea true comparison to the KPECE1 standard solution, the crackwas modelled with an embedded elliptical shape. The crackshape aspect ratio was fixed at, a/c = 0.375, and distance fromthe plate internal surface to the centre of the crack was fixed atd1 = 20.0mm. The crack depth, 2a, was then varied from 30mmdown to 5mm. The loading (as per Tab. 2) was applied as anequivalent crack face traction.

The resulting stress intensity factors calculated for eachcrack size using each method are summarized at the critical po-sition on the crack front (φ = 270◦) in Tab. 4. The percentageincrease in stress intensity factor calculated using a crack meshcompared to the standard solution is plotted in Fig. 16 across therange of crack depths.

As can be seen, the large differences calculated in stressintensity factors between the crack mesh and standard solutionreduce as the crack size decreases. However even at relativelysmall crack sizes, a potentially significant difference still exists.

CONCLUSIONAn investigation was carried out to determine the cause of

the difference between the stress intensity factors calculated us-ing the standard solution given in API 579-1/ASME FFS-1, andthose calculated using a FEA with a crack incorporated into themodel.

Three studies were carried out, trialling different idealizedgeometries. The first was a comparison between the stress inten-sity factor calculated for an embedded elliptical crack and an em-bedded constant depth crack (as used in the crack incorporated

5 10 15 20 25 300

20

40

60

80

100

Crack depth, 2a [mm]

Incr

ease

inSt

ress

Inte

nsity

Fact

or[%

]

ϕ = 0◦ / 180◦

ϕ = 90◦

ϕ = 270◦

FIGURE 16: COMPARISON OF INCREASE IN KI AT KEYPOINTS ON THE CRACK FRONT CALCULATED USINGCRACK MESH VERSUS THE STANDARD SOLUTION FORA RANGE OF CRACK SIZES FOR AN EMBEDDED ELLIP-TICAL CRACK IN A PLATE.

into the model). The second study investigated the sensitivity ofthe geometry height on the calculation of the stress intensity fac-tors. The third study explored the sensitivity of the crack size onthe calculation of the stress intensity factor when comparing thecrack mesh and standard solution methods. The validity of thestandard stress intensity factor solution when outside the speci-fied geometry limits was also investigated.

The outcomes of the investigation are summarized below:

• Standard stress intensity factor solutions may still be valideven when outside the specified geometry limits.

• For the geometry assessed, an embedded constant depthcrack gave a 10 to 15% higher stress intensity factor thanfor an embedded elliptical crack. This indicates usingthe standard stress intensity factor solutions for ellipti-cal shaped cracks could result in non-conservatism if thecrack-like flaw has a constant depth.

• The calculation of the stress intensity factor when using acrack mesh increases significantly as the geometry heightreduces and crack size increases, both of which result in areduction in stiffness in the component.

• Idealized (i.e. plate) crack meshes can still produce mean-ingful results if the reduction in stiffness is captured.

7 Copyright c© 2017 by ASME

RECOMMENDATIONSIt is recommended that if using standard stress intensity fac-

tor solutions on a defect that has a constant depth shape, ratherthan elliptical, a FEA of an idealized crack mesh should be car-ried out to evaluate the possible increase in the stress intensityfactors. When using an automatic FEA crack mesh generatorthis comparison can be completed quickly and efficiently.

It is recommended to exercise a high degree of cautionwhen applying standard stress intensity factor solutions to crackswhere the stiffness of the component may be reduced. Planarcrack-like flaws in nozzles are a good example of where this canoccur, as highlighted in this paper.

To confirm the validity of the standard stress intensity factorsolutions, a FEA of an idealized crack mesh can be used, pro-vided it is a reasonable approximation of the true geometry andaccounts for the reduction in stiffness. If the standard solutionsare found to not be valid, then the idealized crack mesh may beable to be used to extract accurate stress intensity factors. How-ever, caution should be exercised when using the stress inten-sity factors calculated away from the location where the drivingstresses were extracted, which may differ significantly. If thefull stress intensity factor distribution around the crack front isrequired, then incorporating a crack into the FEA model is stillrecommended.

References[1] The American Society of Mechanical Engineers and the

American Petroleum Institute. API 579-1/ASME FFS-1.1220 L Street, N.W., Washington, D.C: API Publishing Ser-vices, 2016.

[2] Dassault Systemes Simulia Corp. Abaqus User’s Manual.Version 6.14-3. Johnston, RI.

[3] Quest Integrity Group. FEACrack. Version 3.2.30. Boulder,Colorado. 2016. URL: www.questintegrity.com/software-products/feacrack.

[4] Robert Dodds, et al. Warp3D. Version 17.7.1. University ofIllinois. 2016. URL: www.warp3d.net.

[5] Anderson, T.L., Fracture Mechanics: Fundamentals andApplications. Boca Raton, Florida: CRC Press, Taylor &Francis Group, 2005.

8 Copyright c© 2017 by ASME