asme sec viii d3 nma app-d.pdf

APPENDIX D — NONMANDATORYFRACTURE MECHANICS CALCULATIONS

D-100 SCOPE

Linear elastic fracture mechanics provides the rela-tionships among the applied stress, the fracture tough-ness of the material, and the critical crack size.

This Appendix provides engineering methods for thecalculation of the stress intensity factorKI for variouspostulated crack geometries in thick-walled vessels.

D-200 CRACK LOCATION ANDSTRESSING

D-201 Internal Radial–Longitudinal Cracks

Figure D-200 shows some locations on a pressurevessel where fatigue cracks may develop. Cracks oftype A develop in the main cylinder in the radial–longitudinal plane. The opening stresses are the hoopstresses and the pressure in the crack. These crackstend to develop in a semielliptical shape with an aspectratio a/,, wherea is the maximum crack depth and,is the surface length.

D-202 Cracks Initiating at Internal CrossBores

When connections between a vessel and piping oraccessories are made through a radial hole (cross bore),fatigue cracks tend to develop in the radial–longitudinalplane. In Fig. D-200, crackB is shown developingfrom both sides of the cross bore; this is often thecase, but the growth may not be symmetric. Calculationof the opening stress field is complicated by the stressconcentration due to the hole, and the pressure in thecrack should be considered.

D-203 Internal Radial–CircumferentialCracks

Cyclic loading may lead to fatigue cracking and fastfracture in the threads of a high pressure vessel usinga threaded closure. These fatigue cracks usually initiateat the root of the first loaded thread because of uneven

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load distribution along the length of the thread andthe stress concentration at the thread root. These fatiguecracks usually propagate in the radial–circumferentialplane (see crackC in Fig. D-200). Usually, the highpressure fluid does not act on the faces of this crack.The longitudinal (opening) stress field has a very steepgradient due to the stress concentration at the thread root.

D-204 Internal Cracks at Blind EndClosures

Fatigue cracks may develop on the inside surfaceof the vessel at the stress concentration associated withblind end closures (see crackD in Fig. D-200).

D-205 Crack Initiating at External Surfaces

Fatigue cracks may also develop on the outsidesurface of high pressure vessels due to the combinationof stress concentrations, tensile residual stresses, and/or environmental effects. See cracksE and F in Fig.D-200.

D-300 CRACK ORIENTATION ANDSHAPE

(a) It is assumed that planar cracks develop at highlystressed points of the vessel. The following assumptionson initial crack orientation and shape to be used infatigue crack propagation calculations are not intendedfor the areas of a weld in welded vessels.

(b) Surface cracks of typeA may be assumed to besemielliptical with an aspect ratioa/, equal to 1⁄3.

(c) Surface cracks at cross bores, typeB, may beassumed to be quarter circular or semicircular (see Fig.D-300).

(d) Surface cracks at the root of threads, typeC,should be assumed to be annular even if the end closurehas interrupted threads. This annular (ring) crack isshown in Fig. D-200.

COPYRIGHT American Society of Mechanical EngineersLicensed by Information Handling ServicesCOPYRIGHT American Society of Mechanical EngineersLicensed by Information Handling Services

Fig. D-200 2001 SECTION VIII — DIVISION 3

FIG. D-200 TYPICAL CRACK TYPES

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D-300 APPENDIX D — NONMANDATORY D-401

FIG. D-300 IDEALIZATIONS OF A CRACK PROPAGATING FROM ACROSS-BORE CORNER

(e) The planes in which cracks of typesA, B, andC are assumed to propagate are as defined in Fig. D-200.

(f) Surface cracks of typeD should be assumed tobe annular. The plane of propagation of typeD cracksshould be determined by stress analysis. Cracks willusually propagate in a plane normal to the directionof the maximum range of tensile stress.

The potential change in crack aspect ratio duringcrack growth should be considered in the calculation.

(g) External surface cracks, typeE, should be as-sumed to be semielliptical and cracks of typeF maybe assumed to be either semielliptical or annular.

D-400 METHODS FOR DETERMININGSTRESS INTENSITY FACTOR

(a) Section XI, Article A-3000, of the ASME Boilerand Pressure Vessel Code provides a method for calcu-lating stress intensity factorsKI from membrane andbending stresses determined from stress analysis of theuncracked component. This method is not suitable for

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determining KI for cracks of typeC because of thesevere stress gradient at the root of the thread. It maynot be suitable for cracks of typesB, D, E, and Fbecause of severe stress gradients due to local stressconcentrations. It is suitable for determiningKI forcracks of typeA if the procedures outlined in D-401are followed. The method given in D-401 may alsobe used to calculate the stress intensity factors due tothermal stresses. Paragraph D-402 outlines how themethod given in D-401 can be used for cracks of typeB in a well-radiused cross bore.

(b) More sophisticated techniques for determiningKI

are described for crack typeC in D-403(a).(c) The weight function technique described in D-

405 can be used for all crack types.

D-401 Stress Intensity Factors for InternalRadial–Longitudinal Cracks

This method may be used to calculate stress intensityfactors for cracks of typeA. The same method is also


D-401 2001 SECTION VIII — DIVISION 3 D-401.1

valid for the calculation of stress intensity factors dueto thermal gradients and due to residual stresses. Thismethod is based on Section XI, Article A-3000 [seeD-700(a)]. It may be used to calculate stress intensityfactors at the deepest point on the crack front and ata point near the free surface.

For a surface flaw, the stresses normal to the planeof the flaw at the flaw location are represented by apolynomial fit over the flaw depth by the followingrelationship:

s p A0 + A1 (x/a) + A2 (x/a)2 + A3 (x/a)3 (1)

whereA0, A1, A2,

A3pconstantsapcrack depthxpdistance through the wall measured from

the flawed surface

CoefficientsA0 through A3 shall provide an accuraterepresentation of stress over the flaw plane for allvalues of flaw depths, 0≤ x/a ≤ 1, covered by theanalysis. Stresses from all sources shall be considered.

Stress intensity factors for surface flaws shall becalculated using the cubic polynomial stress relationgiven by Eq. (2):

KI p [(A0 + Ap) G0 + A1G1 + A2G2

+ A3G3] !pa/Q (2)

whereA0, A1, A2,

A3pcoefficients from Eq. (1) that represent thestress distribution over the flaw depth, 0≤x/a ≤ 1. When calculatingKI as a functionof flaw depth, a new set of coefficientsA0

through A3 shall be determined for eachnew value of flaw depth.

Appinternal vessel pressurep, if the pressureacts on the crack surfaces.Ap p 0 forother flaws.

G0, G1,G2, G3pfree surface correction factors from Tables

D-401.1 and D-401.2Qpflaw shape parameter using Eq. (3)apflaw depth

Q p 1 + 4.593 (a/,)1.65 − qy (3)

where,pmajor axis of the flaw

a/,pflaw aspect ratio 0≤ a/, ≤ 0.5

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qypplastic zone correction factor calculated us-ing the following equation:

qy p h [(A0 + Ap)G0 + A1G1 + A2G2 + A3G3] / Sy j 2/6

D-401.1 Alternate Method(a) If the distribution of stresses normal to the crack

surface can be accurately represented by a single equa-tion of the form of Eq. (1) over the entire range ofcrack depths of interest, the following method may beused to calculate the distribution ofKI over this crackdepth.

The stress distribution is represented by

s p A ′0 + A ′1(x/t) + A ′2(x/t)2 + A ′3(x/t)3 (4)

For each value ofa/t, the values ofA ′i are convertedto Ai values as follows.

A0 p A ′0

A1 p A ′1(a/t)

A2 p A ′2(a/t)2

A3 p A ′3(a/t)3

TheseAi values are then used in Eq. (2) to calculateKI.(b) For a plain cylinder remote from any discontinu-

ity, and for diameter ratios between 1.2 and 3.0, thevalues of A ′i for calculating KI due to pressure onlymay be calculated from the following equations [seeD-700(b)].

A ′0/P p (Y2 + 1)/(Y2 − 1)

A ′1/P p 1.051 − 2.318Y + 0.3036Y2 − 0.004417Y3

A ′2/P p −1.7678 + 0.9497Y + 0.9399Y2 − 0.2056Y3

A ′3/P p −0.2798 + 1.3831Y − 1.2603Y2 + 0.2138Y3

01


APPENDIX D — NONMANDATORY Table D-401.1

TABLE D-401.1COEFFICIENTS G0 THROUGH G3 FOR SURFACE CRACK AT DEEPEST POINT

Flaw Aspect Ratioa/,

Coefficient a/t 0.0 0.1 0.2 0.3 0.4 0.5

Uniform 0.00 1.1208 1.0969 1.0856 1.0727 1.0564 1.0366G0 0.05 1.1461 1.1000 1.0879 1.0740 1.0575 1.0373

0.10 1.1945 1.1152 1.0947 1.0779 1.0609 1.03960.15 1.2670 1.1402 1.1058 1.0842 1.0664 1.04320.20 1.3654 1.1744 1.1210 1.0928 1.0739 1.04820.25 1.4929 1.2170 1.1399 1.1035 1.0832 1.05430.30 1.6539 1.2670 1.1621 1.1160 1.0960 1.06140.40 2.1068 1.3840 1.2135 1.1448 1.1190 1.07720.50 2.8254 1.5128 1.2693 1.1757 1.1457 1.09310.60 4.0420 1.6372 1.3216 1.2039 1.1699 1.10580.70 6.3743 1.7373 1.3610 1.2237 1.1868 1.11120.80 11.991 1.7899 1.3761 1.2285 1.1902 1.1045

Linear 0.00 0.7622 0.6635 0.6826 0.7019 0.7214 0.7411G1 0.05 0.7624 0.6651 0.6833 0.7022 0.7216 0.7413

0.10 0.7732 0.6700 0.6855 0.7031 0.7221 0.74180.15 0.7945 0.6780 0.6890 0.7046 0.7230 0.74260.20 0.8267 0.6891 0.6939 0.7067 0.7243 0.74200.25 0.8706 0.7029 0.7000 0.7094 0.7260 0.74510.30 0.9276 0.7193 0.7073 0.7126 0.7282 0.74680.40 1.0907 0.7584 0.7249 0.7209 0.7338 0.75110.50 1.3501 0.8029 0.7454 0.7314 0.7417 0.75660.60 1.7863 0.8488 0.7671 0.7441 0.7520 0.76310.70 2.6125 0.8908 0.7882 0.7588 0.7653 0.77070.80 4.5727 0.9288 0.8063 0.7753 0.7822 0.7792

Quadratic 0.00 0.6009 0.5078 0.5310 0.5556 0.5815 0.6084G2 0.05 0.5969 0.5086 0.5313 0.5557 0.5815 0.6084

0.10 0.5996 0.5109 0.5323 0.5560 0.5815 0.60850.15 0.6088 0.5148 0.5340 0.5564 0.5815 0.60870.20 0.6247 0.5202 0.5364 0.5571 0.5815 0.60890.25 0.6475 0.5269 0.5394 0.5580 0.5817 0.60930.30 0.6775 0.5350 0.5430 0.5592 0.5820 0.60990.40 0.7651 0.5545 0.5520 0.5627 0.5835 0.61150.50 0.9048 0.5776 0.5632 0.5680 0.5869 0.61440.60 1.1382 0.6027 0.5762 0.5760 0.5931 0.61880.70 1.5757 0.6281 0.5907 0.5874 0.6037 0.62550.80 2.5997 0.6513 0.6063 0.6031 0.6200 0.6351

Cubic 0.00 0.5060 0.4246 0.4480 0.4735 0.5006 0.5290G3 0.05 0.5012 0.4250 0.4482 0.4736 0.5006 0.5290

0.10 0.5012 0.4264 0.4488 0.4736 0.5004 0.52900.15 0.5059 0.4286 0.4498 0.4737 0.5001 0.52890.20 0.5152 0.4317 0.4511 0.4738 0.4998 0.52890.25 0.5292 0.4357 0.4528 0.4741 0.4994 0.52890.30 0.5483 0.4404 0.4550 0.4746 0.4992 0.52910.40 0.6045 0.4522 0.4605 0.4763 0.4993 0.52980.50 0.6943 0.4665 0.4678 0.4795 0.5010 0.53160.60 0.8435 0.4829 0.4769 0.4853 0.5054 0.53490.70 1.1207 0.5007 0.4880 0.4945 0.5141 0.54070.80 1.7614 0.5190 0.5013 0.5085 0.5286 0.5487

GENERAL NOTE: Interpolations in a/t and a/, are permitted.

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Table D-401.2 2001 SECTION VIII — DIVISION 3

TABLE D-401.2COEFFICIENTS G0 THROUGH G3 FOR SURFACE CRACK AT FREE SURFACE

Flaw Aspect Ratioa/,

Coefficient a/t 0.0 0.1 0.2 0.3 0.4 0.5

Uniform 0.00 . . . 0.5450 0.7492 0.9024 1.0297 1.1406G0 0.05 . . . 0.5514 0.7549 0.9070 1.0330 1.1427

0.10 . . . 0.5610 0.7636 0.9144 1.0391 1.14730.15 . . . 0.5738 0.7756 0.9249 1.0479 1.15450.20 . . . 0.5900 0.7908 0.9385 1.0596 1.16410.25 . . . 0.6099 0.8095 0.9551 1.0740 1.17630.30 . . . 0.6338 0.8318 0.9750 1.0913 1.19090.40 . . . 0.6949 0.8881 1.0250 1.1347 1.22780.50 . . . 0.7772 0.9619 1.0896 1.1902 1.27460.60 . . . 0.8859 1.0560 1.1701 1.2585 1.33150.70 . . . 1.0283 1.1740 1.2686 1.3401 1.39840.80 . . . 1.2144 1.3208 1.3871 1.4361 1.4753

Linear 0.00 . . . 0.0725 0.1038 0.1280 0.1484 0.1665G1 0.05 . . . 0.0744 0.1075 0.1331 0.1548 0.1740

0.10 . . . 0.0771 0.1119 0.1387 0.1615 0.18160.15 . . . 0.0807 0.1169 0.1449 0.1685 0.18930.20 . . . 0.0852 0.1227 0.1515 0.1757 0.19710.25 . . . 0.0907 0.1293 0.1587 0.1833 0.20490.30 . . . 0.0973 0.1367 0.1664 0.1912 0.21280.40 . . . 0.1141 0.1544 0.1839 0.2081 0.22890.50 . . . 0.1373 0.1765 0.2042 0.2265 0.24530.60 . . . 0.1689 0.2041 0.2280 0.2466 0.26200.70 . . . 0.2121 0.2388 0.2558 0.2687 0.27910.80 . . . 0.2714 0.2824 0.2887 0.2931 0.2965

Quadratic 0.00 . . . 0.0254 0.0344 0.0423 0.0495 0.0563G2 0.05 . . . 0.0264 0.0367 0.0456 0.0538 0.0615

0.10 . . . 0.0276 0.0392 0.0491 0.0582 0.06660.15 . . . 0.0293 0.0419 0.0527 0.0625 0.07160.20 . . . 0.0313 0.0450 0.0565 0.0669 0.07640.25 . . . 0.0338 0.0484 0.0605 0.0713 0.08120.30 . . . 0.0368 0.0521 0.0646 0.0757 0.08580.40 . . . 0.0445 0.0607 0.0735 0.0846 0.09460.50 . . . 0.0552 0.0712 0.0834 0.0938 0.10300.60 . . . 0.0700 0.0842 0.0946 0.1033 0.11090.70 . . . 0.0907 0.1005 0.1075 0.1132 0.11830.80 . . . 0.1197 0.1212 0.1225 0.1238 0.1252

Cubic 0.00 . . . 0.0125 0.0158 0.0192 0.0226 0.0261G3 0.05 . . . 0.0131 0.0172 0.0214 0.0256 0.0297

0.10 . . . 0.0138 0.0188 0.0237 0.0285 0.03320.15 . . . 0.0147 0.0206 0.0261 0.0314 0.03650.20 . . . 0.0159 0.0225 0.0285 0.0343 0.03980.25 . . . 0.0173 0.0245 0.0310 0.0371 0.04290.30 . . . 0.0190 0.0267 0.0336 0.0399 0.04590.40 . . . 0.0234 0.0318 0.0390 0.0454 0.05150.50 . . . 0.0295 0.0379 0.0448 0.0509 0.05650.60 . . . 0.0380 0.0455 0.0513 0.0564 0.06110.70 . . . 0.0501 0.0549 0.0587 0.0621 0.06520.80 . . . 0.0673 0.0670 0.0672 0.0679 0.0687

GENERAL NOTE: Interpolations in a/t and a/, are permitted.

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D-402 Stress Intensity Factors for CracksInitiating at Cross Bores

The stress intensity factors for cracks of typeB maybe calculated using the method given in D-401, providedthat the intersection of the cross bore with the boreof the main cylinder is radiused at least one-fourth ofthe diameter of the cross bore. See D-700(c). Thevalues of stresses to be used to obtain the polynomialfit in Eq. (1) of D-401 are determined as follows.

(a) Elastic stress analysis may be used to determinethe stress field in the vicinity of the uncracked crossbore. This elastic analysis is used to obtain the directstresses acting normal to the plane of the assumedcrack. The distribution of these stresses along lineb–b in Fig. D-200 shall be used to obtain the polynomialfit in Eq. (1) of D-401. As shown in Fig. D-200, thecross bore corner crack is assumed to be equivalentto a semicircular crack (a/, p 0.5) in a plane withthe line b–b as the axis of symmetry.

(b) If residual stresses have been introduced, suchas by autofrettaging the main cylinder, theK due toresidual stresses may be calculated using the polynomialfitting technique in D-401 with the simplifying assump-tion that the tangential residual stress distribution inthe main cylinder acts along lineb–b.

D-403 Stress Intensity Factors for InternalRadial–Circumferential Cracks

This method applies only to crack depths within thelimits of KD-412 and where pressure is not acting onthe crack faces.

Type C fatigue cracks usually initiate at the root ofthe first fully loaded thread. This should be confirmedby calculation of the load distribution and by detailedstress analysis of the first and any other heavily loadedthreads. To calculate theKI for a thread root crackgrowing in the radial–circumferential plane, the distribu-tion of longitudinal stresss,(x) from the thread rootthrough the thickness of the uncracked wall shouldbe determined. For this analysis, the threads may beconsidered as annular grooves. If interrupted threadsare used (see KD-631.6), it is not necessary to accountfor the stress concentrations at the ends of the interruptedthreads, since it is assumed that all cracks of typeCare annular.

(a) In the Buchalet–Bamford method [see D-700(d)and (e)], the distribution of direct stresses normal tothe plane containing the annular crack is approximatedby a third-order polynomial.

251

s,(x) p A0 + A1x + A2x2 + A3x

3 (1)

wherex is the radial distance from the free surface ofthe crack.

The stress distribution determined by a linear elasticanalysis is calculated first and then the four coefficients(A0, A1, A2, A3) in Eq. (1) are chosen to give the bestcurve fit. After the values ofA0, A1, A2, and A3 arechosen, Eqs. (2)–(6) are used to calculate the stressintensity factorKI for various crack depthsa.

KI p ! pa 1A0F1 +2aA1F2

p+

a2A2F3

2+

4a3A3F4

3p 2 (2)

F1, F2, F3, andF4 are the magnification factors relativeto the geometry considered. These magnification factorsare given in Fig. D-403.1 as a function of relativecrack depth or can be calculated by the followingequations.

F1 p 1.1259 + 0.2344(a/t) + 2.2018(a/t)2

− 0.2083(a/t)3 (3)

F2 p 1.0732 + 0.2677(a/t) + 0.6661(a/t)2

+ 0.6354(a/t)3 (4)

F3 p 1.0528 + 0.1065(a/t) + 0.4429(a/t)2

+ 0.6042(a/t)3 (5)

F4 p 1.0387 − 0.0939(a/t) + 0.6018(a/t)2

+ 0.3750(a/t)3 (6)

(b) In some cases, a single third-order polynomial[Eq. (1)] will not be sufficient to fit the stress distributionin the region of interest. It is possible to split thedistribution into several regions. Figure D-403.2 showsan example where the region of interest has beendivided into two regions where the stress in each regionis represented by a different polynomial. The valuesfor KI are calculated using Eq. (2) for each regionwith the appropriate polynomial for that region.

(c) It is important that there not be a discontinuityin the value ofKI where two regions join. For instance,since the values ofA0, A1, A2, andA3 in the polynomialfor region 2 are different from the values ofA0, A1,A2, andA3 in the polynomial for region 1, two differentvalues ofKI will be calculated at the point where thetwo regions join. To compensate for the discontinuityin the value of KI where the two regions join, thedifference at the discontinuityDKI is added to thecalculated values of all subsequent values ofKI. This


D-403 2001 SECTION VIII — DIVISION 3 D-405

FIG. D-403.1 MAGNIFICATION FACTORS FOR CIRCUMFERENTIAL CRACK

will then produce the curve shown in Fig. D-403.3and given by Eq. (7).

KIcorr p ! pa 1A0F1 +2aA1F2

p+

a2A2F3

2

+4a3A3F4

3p 2 + SDKI (7)

where ∑DKI is the sum of all DK’s for precedingregions. TheDK for the first region (at the free surface)is 0.

D-404 Stress Intensity Factors for Cracks ofTypes D, E, and F

(a) The stress intensity factors for cracks of typesD, E, andF may be calculated using the method givenin D-401.

(b) For cracks of typesD and F, the distribution ofstresses normal to the plane of the crack which wouldexist in the uncracked component should be determinedusing a stress analysis such as finite element analysis.

(c) For cracks of typeE, the tangential stressescalculated using the Lame´ equations may be used for

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calculating the stress intensity factor due to internalpressure.

D-405 Stress Intensity Factors Determinedby Weight Function Methods

The weight function method can be used for alltypes of cracks.

For the annular (ring) cracks considered in D-403,the crack tip stress intensityKI can be written as:

KI p Ea

0s,(x) w(x,a)dx

wheres, (x) is the longitudinal stress distribution alongthe x-axis (see Fig. D-200) andw(x,a) is the Buecknerweight function. This weight function is unique forthis cracked geometry and is independent of the loadingfrom which it is derived. Therefore, the weight functioncan be written as



FIG. D-403.2 POLYNOMIAL REPRESENTATION OF STRESSDISTRIBUTION

w(x,a) pH

2KIREF 1dVREF(x,a)da 2

whereVREF is the surface opening displacement in the, (longitudinal) direction andKIREF is the crack tipstress intensity factor derived for this geometry and aless complex loading, e.g., uniform stress normal tothe crack plane. For plane stressH p E and for planestrain H p E(1 − n2).

Approximate methods have been developed for ob-taining the crack opening displacement fieldVREF fora ring crack in a simple cylinder. These values ofVREF

and the associated stress intensity factorsKREF can beused to derivew(x,a), which can then be used to deriveKI for the ring crack at the thread root.

D-500 CALCULATION OF FATIGUECRACK GROWTH RATES

(a) In accordance with KD-430, the fatigue crackgrowth rate shall be calculated from

253

dadN

p C[f (RK)] (DK)m

(b) The function ofRK is different for positive andfor negative values ofRK, and for different materials.For materials listed in Table D-500 the followingfunctions of RK may be used.

For RK ≥ 0,

f (RK) p 1 + C3RK

For RK < 0,

f (RK) p [C2/(C2 − RK)]m

(c) The values of the constantsC and m for somematerials are given in Table KD-430. The values ofthe remaining constants given in Table D-500 shouldbe used for the materials listed.

(d) For austenitic stainless steels, the values ofCand m are given in KD-440, Table KD-430, andf (RK)


Fig. D-403.3 2001 SECTION VIII — DIVISION 3 Table D-500

FIG. D-403.3 METHOD OF CORRECTING KI AT DISCONTINUITIESBETWEEN REGIONS

TABLE D-500CRACK GROWTH RATE FACTORS

Material C3 C2

High strength low alloy steels, 3.53 1.5Sy > 90 ksi

13Cr–8Ni–2Mo (precipitation 3.06 1.5hardened)

17Cr–4Ni–4Cu (precipitationhardened), Sy > 135 ksi

RK < 0.67 3.48 1.5RK > 0.67 f(RK) p 30.53RK − 17.0

254



should be calculated as follows: for 0≥ RK, f (RK)p 1.0;for 0.79≥RK>0, f (RK)p1.0+1.8RK; for 1.0>RK>0.79,f (RK)p−43.35+57.97RK.

(e) Other values of these constants may be used ifthey can be justified by standard fatigue crack propaga-tion tests conducted at the appropriateRK ratios.

(f) The number of cycles for fatigue crack propaga-tion may be calculated by numerical integration of theappropriate crack growth equation by assuming thatthe value ofK is constant over an interval of crackgrowth Da which is small relative to the crack depthat that point. To ensure that the interval of crack depthis sufficiently small, the calculation should be repeatedusing intervals of decreasing size until no significantchange in the calculated number of design operatingcycles is obtained.

D-600 FRACTURE TOUGHNESSCORRELATIONS

(a) The value of the fracture toughness to be usedin the calculations in Article KD-4 is the plane strainfracture toughnessKIc. If values of KIc or anothermethod for determiningKIc is given in Part KM forthe specific material to be used, these values shouldbe used. Otherwise, if the MDMT is demonstrated tobe on the upper shelf for the material being used, thevalue of KIc should be calculated from the Charpy V-notch energy (CVN) values given in Part KM usingthe following equation:

(KIc/Sy)2 p 5.0 (CVN/Sy − 0.05)

whereSy is the yield strength, ksi;CVN is the CharpyV-notch impact strength, ft-lb; andKIc is the fracturetoughness, ksi! in.

(b) Conversions of values obtained from other tough-ness tests toKIc should be performed using the followingequations.

(1) Equivalence ofKIc and JIc:

255

KIc p ! EJIc (plane stress)

KIc p ! EJIc

(1 − n2)(plane strain)

(2) Equivalence of crack tip opening displacement(CTOD) and KIc:

KIc p ! (CTOD)ESy

whereEp modulus of elasticitySyp yield strengthnp Poisson’s ratio

D-700 REFERENCES

(a) Cipolla, R. C. Technical Basis for the RevisedStress Intensity Factor Equation for Surface Flaws inASME Section XI, Appendix A.ASME PVP-Vol. 313-1, 1995: 105–121.

(b) Kendall, D. P. Application of the New SectionXI, A-3000 Method for Stress Intensity Factor Calcula-tion to Thick-Walled Pressure Vessels.ASME PVP-Vol. 335, 1996: 189–194

(c) Chaaban, A. and Burns, D. J.Design of HighPressure Vessels With Radial Crossbores.Physica B139and 140; 1986: 766–772

(d) Buchalet, C. B. and Bamford, W. H.StressIntensity Factor Solutions for Continuous Surface Flawsin Reactor Pressure Vessels, Mechanics for CrackGrowth. ASTM STP 590, 1976: 385–402

(e) Perez, E. H.; Sloan, J. G.; and Kelleher, K. J.Application of Fatigue Crack Growth to an IsostaticPress.ASME PVP-Vol. 125, 1987: 53–61

(f) Barsom, J. M. and Rolfe, S. T.CorrelationsBetween KIc and Charpy V-Notch Test Results in theTransition Temperature Range.ASTM STP 466, 1970:281–302

(g) Rolfe, S. T. and Novak, S. R.Slow-Bend KIcTesting of Medium-Strength High-Toughness Steels.ASTM STP 463, 1970: 124–159

(h) Kapp, J. A. and Underwood, J. H.CorrelationBetween Fracture Toughness, Charpy V-Notch ImpactEnergy, and Yield Strength for ASTM A 723 Steel.ASME PVP-Vol. 283, 1992: 219–222


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