ARTICLE KD-4FRACTURE MECHANICS EVALUATION

KD-400 SCOPE

This Article presents a fracture mechanics designapproach. In accordance with KD-140, if it can beshown that the vessel will fail in a leak-before-burstmode, then the number of design cycles shall becalculated in accordance with either Article KD-3 orArticle KD-4. If a leak-before-burst mode of failurecannot be shown, then the number of design cyclesshall be calculated in accordance with this Article.

KD-401 General

(a) This Article is based on the assumption that thecrack initiation stage is complete and that cracks existat highly stressed points in the pressure vessel. Theprinciples of linear elastic fracture mechanics were usedto develop the criteria in this Article for calculatingthe number of design cycles to propagate these cracksto the critical crack depth and the maximum allowabledepth. See also Nonmandatory Appendix D.

(b) Manufacturing processes such as welding, heattreatment, forming, autofrettage, shrink fitting, and wirewrapping introduce residual stresses. Some cracks maypropagate through the resulting residual stress field dueto cyclic loading. A method for accounting for theseresidual stresses is given in KD-420.

(c) The critical crack depth for a given loadingcondition is defined to be the crack depth at whichthe stress intensity factor equalsKIc . The critical crackdepth shall be calculated for the most severe combina-tion of loading conditions. If the critical crack depthis less than the wall thickness, it may not be possibleto assume a leak-before-burst mode of failure. However,see KD-141.

KD-410 CRACK SIZE CRITERIA

KD-411 Assumed Initial Crack Size

(a) The initial crack size to be used for the calculationof the crack propagation design cycles shall be based

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on the nondestructive examination method to be used.If the nondestructive examination method to be usedmeasures the length of a surface indication, an assump-tion shall be made as to the depth and shape of anassumed initial crack.

(b) A surface crack not associated with a stressconcentration shall be assumed to be semielliptical witha ratio of depth to surface length of 1:3. The assumedsurface length shall not be less than the maximumacceptable nondestructive examination indication asgiven in Part KE unless a smaller length is specifiedin the User’s Design Specification [see KG-311.12(a)].If a smaller length is specified, it must be clearlydemonstrated that the nondestructive examinationmethod used will reliably detect indications of that size.

(c) For a thread root or circumferential groove, thecrack shall be assumed to be annular. The initial crackdepth shall be assumed to be not less than one-thirdof the maximum acceptable length of a surface nonde-structive examination indication as defined above.

KD-412 Allowable Final Crack Depth

To calculate the number of design cyclesNp basedon crack propagation, it is necessary to determine anallowable final crack depth. The allowable final crackdepth shall be calculated in accordance with KD-412.1and KD-412.2. The calculated number of design cyclesis the number of cycles required to propagate a crackof the assumed initial flaw size to that allowable finalcrack depth. The calculated number of design cyclesis defined as the lesser of:

(a) the number of cycles corresponding to one-halfof the number of cycles required to propagate a crackfrom the initial assumed flaw size to the critical cracklength [see KD-401(c)]; or

(b) the number of cycles required to propagate acrack from the initial assumed flaw size to the depthas defined in KD-412.1 and KD-412.2.

KD-412.1 Monobloc Vessels.For monobloc vessels,the allowable final crack depth shall be the lesser of

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KD-412.1 2001 SECTION VIII — DIVISION 3 KD-440

25% of the section thickness being considered or 25%of the critical crack depth.

KD-412.2 Vessels With Two or More Layers(a) For vessels with two or more layers, the final

crack depth in the inner layer may be equal to the layerthickness, provided the theoretical collapse pressure (twotimes the value calculated in KD-251.2) of the combinedremaining layers is at least 20% higher than the designpressure of the unflawed vessel.

Otherwise, the allowable final crack depth shall notexceed 25% of the inner layer thickness.

The theoretical collapse pressure of the combinedremaining layers shall be calculated using the insidediameter of the innermost of the remaining layers asthe pressure loading diameter.

(b) For all other layers, the allowable final crackdepth shall not exceed 25% of the layer thicknessexcept as in KD-412.2(c).

(c) The allowable final crack depth of the outermostlayer also shall not exceed 25% of the theoreticalcritical crack depth.

KD-420 STRESS INTENSITY FACTOR KI

CALCULATION

(a) Methods for calculating the fracture mechanicsstress intensity factor for several critical locations ina typical high pressure vessel are given in NonmandatoryAppendix D.

(b) All forms of loading shall be considered, includ-ing pressure stresses, thermal stresses, discontinuitystresses, and residual stresses. In some cases, the stressesproduced by the action of the fluid pressure in thecrack shall be considered. Guidelines are given inNonmandatory Appendix D.

(c) The KI values for all loadings except residualstresses shall be assessed by considering their minimumand maximum values and their chronological relation-ship. The combined effects of these loadings shall bereported as minimumK*

I min and maximumK*I max stress

intensity factors. The effects of intentionally introducedresidual stresses, such as those due to autofrettage,shrink fitting, or wire winding, shall be assessed sepa-rately by calculating an equivalent positive or negativestress intensity factor due to these residual stressesKI res. KD-430 specifies howKI res, K*

I min, and K*I max

are combined to calculate a crack growth rate whichshall be integrated to solve for a calculated number ofdesign cyclesNp based on crack propagation.

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KD-430 CALCULATION OF CRACKGROWTH RATES

(a) The crack growth rateda/dN is assumed to bea function of the range of stress intensity factorDKand the stress intensity factor ratioRK where

dadN

p C [f (RK)] (DK)m (1)

DK p K*I max − K*

I min

and

RK pK*

I min + KI res

K*I max + KI res

If (K*Imax + K*

Ires) ≤ 0, da/dN may be assumed to beequal to zero. The values ofC and m to be used forsome materials are given in Table KD-430 for the caseof f (RK) p 1. If RK p 0, then f (RK) p 1. Therelationshipf (RK), which may be used for some materi-als, is given in Nonmandatory Appendix D.

(b) If the value of DK is less than the value of thethresholdDK (DKth) as given by the following equation,the value ofda/dN may be assumed to be zero.

DKth p the lesser ofG (1 − HRK) ksi-in.1⁄2 or

I ksi-in.1⁄2, but is not less than 2 ksi-in.

1⁄2

Values of G, H, and I for some common pressurevessel materials are given in Table KD-430.

KD-440 CALCULATED NUMBER OFDESIGN CYCLES

Crack growth is dependent on both cyclic stress andthe crack length when the cycle occurs. Thus, thecalculated number of design cyclesNp is highly depen-dent on the sequence of loadings. The designer shallprovide a summary of the sequence and magnitude ofall loadings and a projection of the calculated crackgrowth associated with each point in the loading se-quence. This summary shall be documented in theManufacturer’s Design Report. See Nonmandatory Ap-pendix B for recalculation of fatigue life based on theactual sequence and magnitude of loading.

The number of design cycles may be calculated bynumerical integration of the crack growth rate [KD-430(a) Eq. (1)]. It shall be assumed thatKI values are

01

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KD-440 PART KD — DESIGN REQUIREMENTS KD-440

TABLE KD-430CRACK GROWTH RATE FACTORS

Material C m G H I

High strength low alloy steels, 1.95E−10 3.26 6.4 0.85 5.5Sy > 90 ksi

13Cr–8Ni–2Mo 9.30E−10 2.70 6.4 0.85 5.5(precipitation hardened)

17Cr–4Ni–4Cu (precipitation 2.38E−10 3.15 6.4 0.85 5.5hardened)

Austenitic stainless steel 1.1E−10 3.30 NA(1) NA(1) NA(1)

NOTE:(1) Threshold values for austenitic stainless steels have not yet been established.

constant over an interval of crack growthDa that issmall relative to the crack depth. To ensure that theinterval of crack depth is sufficiently small, the calcula-

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tion shall be repeated using intervals of decreasing sizeuntil no significant change in the calculated numberof design cyclesNp is obtained.

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