ARTICLE KD-9SPECIAL DESIGN REQUIREMENTS FOR WIRE-WOUND VESSELS AND WIRE-WOUND FRAMES

KD-900 SCOPE

The requirements of this Article apply specificallyto pressure vessels consisting of an inner cylinder (ora number of concentric cylinders) prestressed by asurrounding winding consisting of at least ten layers.The end load is not carried by the cylinder(s) or thewinding. The winding consists of a wire helically woundedge-to-edge in pretension in a number of turns andlayers around the outside of the cylinder. These require-ments also apply to wire-wound frames used to carrythe load from the closures. See Fig. KD-900.

The special requirements are in addition to the generalrequirements given in Articles KD-2, KD-3, and KD-4.

KD-910 STRESS ANALYSIS

The stresses in the vessel due to the internal pressureshall be calculated in accordance with Articles KD-1and KD-2.

The calculation of the prestressing of the cylindershall be based on a winding procedure that specifiesthe wire force that has to be used for each windinglayer at the application (see KF-913). The calculationshall give the decrease of the inner diameter of thecylinder and the residual stresses at all points of thevessel wall induced by the winding operation. Equationsfor this calculation are given in KD-911.

A corresponding winding procedure and stress calcu-lation for the wire-wound frame shall give the decreaseof a reference length of the frame and residual principalstresses in the frame and at the different layers of thewinding.

The calculated decrease of the inner diameter andthe reference length of the frame shall be determinedin intervals and shall be used for comparison with theresults from corresponding measurements made duringthe winding operation.

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KD-911 Residual Stresses and Deflections inCylinders Due to Flat Wire Winding

The equations in this paragraph are valid for flatwire with rectangular cross section wound edge-to-edge. For other wire shapes, appropriate correctionsshall be made. It is assumed that the winding operationis performed with the stressSw(x) in the wire and thatthis stress is a function of the diameter coordinatex(see Fig. KD-911). When the winding layers are appliedbetweenx p Dif and x p Dw, then the followingtangential stressesst(x1), radial stressessr(x1), anddiametral deformationd are introduced at the diameterx1 of the inner cylinders:

st(x1) p − 31 + 1DI

x122

4 ED

w

Dif1 x

x2 − D2I

Sw(x)2 dx

sr(x1) p − 31 − 1DI

x122

4 ED

w

Dif1 x

x2 − D2I

Sw(x)2 dx

d p −2DI

E EDw

Dif1 x

x2 − D2I

Sw(x)2 dx

whereDIp inside diameterDif p diameter of the interface between cylinder and

windingDOp outside diameter after finished winding oper-

ationDwp instantaneous applied outside diameter of

windingEp modulus of elasticityx1p any diameter of the cylinderx2p any diameter of the winding

NOTE: Any consistent system of units may be used.

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Fig. KD-900 2001 SECTION VIII — DIVISION 3

FIG. KD-900 WIRE-WOUND VESSEL AND FRAME CONSTRUCTION

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KD-911 PART KD — DESIGN REQUIREMENTS KD-923

FIG. KD-911 NOMENCLATURE FOR WIRE-WOUND CYLINDERS

The corresponding stresses introduced in the windingarea at the diameterx2(<Dw) of the winding are:

st(x2) p Sw(x2) − 31 + 1DI

x222

4 ED

w

x21 x

x2 − D2I

Sw(x)2 dx

sr(x2) p − 31 − 1DI

x222

4 ED

w

x21 x

x2 − D2I

Sw(x)2 dx

The equations given above are valid as long as:(a) the helix angle of the winding is less than 1.0 deg;(b) the maximum gap between the wires in the

longitudinal direction of the vessel is less than 5% ofthe wire width, or 0.010 in. (0.25 mm), whichever isless; and

(c) neither the liner nor the wire yields. See KD-920.

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KD-912 Stress in Wire Wound Frames

Because of the many possible geometric forms offrames, specific equations are not given here. Suchframes shall satisfy the requirements of Articles KD-2, KD-3, and KD-4.

KD-920 STRESS LIMITS

KD-921 Diameter Ratio of Vessel Wall

When flat wire with rectangular cross section is used,the overall diameter ratio shall not be lower than thelimit given by the equation in KD-251.2. For otherwire shapes, corrections shall be made.

KD-922 Stress Intensity Limits for InnerCylinder(s) and Wire

Under design conditions, the average stress intensityover the cross section of each individual wire at anypoint in the winding shall not exceed the local primarymembrane stress limit,PL, given in Fig. KD-230.

For welded wire joints (see KF-912), the correspond-ing average stress intensity shall not exceed two-thirdsof the local primary membrane stress limit,PL, givenin Fig. KD-230, whereSy is the yield strength of theunwelded wire material.

The calculated primary-plus-secondary stress intensityfor the inner cylinder(s) shall not exceedSy at anyvalue of pressure from atmospheric to design pressureat any specified coincident temperature, or at any valueof pressure from atmospheric to test pressure at thetest temperature.

KD-923 Minimum Level of Prestressing ofFrames Made From Columns andYokes

In the case when the frame is made up of nonintegralcolumns and yokes, the prestressing of the frame bythe winding shall be high enough to ensure that theyokes and columns are in mechanical contact even ata load corresponding to 105% of the pressure to beapplied at the hydrostatic test (see Article KT-3). Thisrequirement shall be checked by calculation and docu-mented in the Manufacturer’s Data Report.

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KD-930 2001 SECTION VIII — DIVISION 3 KD-932.3

KD-930 FATIGUE EVALUATION

KD-931 General

(a) A calculation to determine the number of designcycles shall be performed for the different componentsof wire-wound vessels and frames in accordance withthe methods stated in Article KD-3. However, an excep-tion has to be made for the winding, which is madeof a material with properties quite different from thoseof the materials on which the curves in Article KD-3are based. The fatigue life of the winding shall insteadbe calculated in accordance with the rules stated inKD-932. A mean stress correction factor shall be appliedto the inner layer in accordance with KD-310 exceptif the liner is of welded construction.

For environmental conditions not covered by thederived design fatigue curve, the Manufacturer shallobtain supplementary fatigue test data.

(b) The same general methods and requirements forfracture mechanics evaluation as in Article KD-4 shallbe applied to wire-wound vessels and frames, exceptthat fracture mechanics evaluation is not required forthe wire itself.

KD-932 Derivation of a Design Fatigue Curvefor Wire

The design fatigue lifeND of the winding is definedas the number of operating cycles when the probabilityis 10% that the calculated average distance betweenfatigue cracks in the wire is 6,500 ft. The design fatiguecurve for wire shall be derived in the way stated inKD-932.1 through KD-932.3 (see Fig. KD-932).

KD-932.1 Wire Fatigue Curve. The calculation ofthe design fatigue life of the winding shall be basedon a wire fatigue curve derived as follows.

(a) Make fatigue tests with wire pieces with a lengthof at least 30 times the maximum cross sectionaldimension, taken from wire coils delivered from thesame manufacturer and produced from the same materialquality and by the same manufacturing method as thewire to be used in the vessel or frame.

(b) Select a mean stress which will avoid bucklingthe test specimen. Make all tests at this mean stressfor all stress amplitudes used.

(c) Make the tests at no less than four levels ofstress amplitudeS with at least six wire pieces at eachstress level. The cyclic rate of the test shall be suchthat appreciable heating of the wire does not occur.Note the number of cyclesNf to complete fatiguerupture.

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(d) Plot the points of correspondingS and Nf on asemilog graph and draw a best-fit curveSf p f (logNf ) based on these points.

(e) Transform this curve to a wire fatigue curveSf ′ p f (log Nf ) valid at mean stressp 0 using theequation

Sf ′ p Sf + Ksbsnm

where snm is the associated mean stress used in thetest (see KD-312.3). The value ofb shall be 0.2 unlessexperimental evidence justifies another value.Ks iscalculated according to Eq. (1) in KD-932.3.

KD-932.2 Design Fatigue Curve.The design fatiguecurve Sa p f (log ND) shall be derived from the wirefatigue curve as stated in KD-932.2(a) through (c).

(a) Divide the Sf ′ values of the wire fatigue curveby a design factorKs, the value of which shall bedetermined as stated in Eq. (1) in KD-932.3, and plotthe curve:

Sa′ p Sf ′ /KS p f2 (log ND)

(b) Divide the Nf values of the wire fatigue curveby a design factorKN, the value of which shall bedetermined as stated in Eq. (2) in KD-932.3, and plotthe curve:

Sa″ p f3 [log (Nf /KN)] p f3 (log ND)

(c) The design fatigue curve,Sa p f (log ND), isthe lower of the two valuesSa′ or Sa″ for all valuesof ND in KD-932.2(a) and (b).

KD-932.3 Design FactorsKS and KN. The valuesof the design factorsKS andKN are multiples of factorswhich account for the effects of stressed length andof scatter in fatigue strength of the wire. They shallbe determined as stated below:

KS p KSLKSS (1)

whereKSL is the factor for the effect of stressed lengthandKSSis the factor for the effect of statistical variation(scatter) in fatigue strength:

KSL p (LW/LT)1⁄30 (2)

where LW is the accepted average distance betweenwire cracks atN p ND and a crack probability of10% (see KD-932) andLT is the length of the wirepieces at the fatigue tests (see KD-932.1). Assuming

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PART KD — DESIGN REQUIREMENTS Fig. KD-932

FIG. KD-932 DERIVATION OF DESIGN FATIGUE CURVE FROM WIRE FATIGUE CURVE

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KD-932.3 2001 SECTION VIII — DIVISION 3 KD-933

a case whereLW equals 6,500 ft andLT equals 0.67ft, the equation givesKSL p 1.35.

KSSp 1/(1 − 1.30Ds) (3)

whereDs is the average value of the relative standarddeviation of the fatigue strength, derived from thescatter at the fatigue test of the wire pieces.

In the calculation ofKSS, the scatter in fatigue strengthis assumed to have a standard Gaussian distribution.

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The value of 1.30 in the equation corresponds to aprobability of 10% for a fatigue crack to occur (seeKD-932).

KN p (KS)4.3 (4)

KD-933 Calculation of Design Fatigue Life ofWinding

The design fatigue curve derived in KD-932 is usedto calculate the design fatigue life of the winding asdescribed in Article KD-3.

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