ASME SEC VIII D3 PART KD-3.pdf

ARTICLE KD-3FATIGUE EVALUATION

KD-300 SCOPE

This Article presents a traditional fatigue analysisdesign approach. In accordance with KD-140, if it canbe shown that the vessel will fail in a leak-before-burst mode, 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 Article KD-4.

KD-301 General

Cyclic operation may cause fatigue failure of pressurevessels and components. While cracks often initiate atthe bore, cracks may initiate at outside surfaces or atlayer interfaces for autofrettaged and layered vessels.In all cases, areas of stress concentrations are a particularconcern. Fatigue-sensitive points shall be identified anda fatigue analysis made for each point. The result ofthe fatigue analysis will be a calculated number ofdesign cyclesNf for each type of operating cycle, anda calculated cumulative effect number of design cycleswhen more than one type of operating cycle exists.

The resistance to fatigue of a component shall bebased on the design fatigue curves for the materialsused. For design fatigue curves, see Fig. KD-320.1 forforged nonwelded construction and Fig. KD-320.2 forwelded construction.

In some cases it may be convenient or necessary toobtain experimental fatigue data for a component itselfrather than for small specimens of the material (seeKD-1260). If there are two or more types of stresscycles which produce significant stresses, their cumula-tive effect shall be evaluated by calculating for eachtype of stress cycle the usage factorsU1, U2, U3, etc.,and the cumulative usage factorU per KD-330. Thecumulative usage factorU shall not exceed 1.0.

KD-302 Theory

The theory used in this Article postulates that fatigueat any point is controlled by the alternating stress

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intensitySalt and the associated mean stresssnm normalto the plane ofSalt . They are combined to define theequivalent alternating stress intensitySeq, which is usedwith the design fatigue curves to establish the numberof design cyclesNf.

KD-302.1 Alternating Stress Intensity.The alternat-ing stress intensitySalt represents the maximum rangeof shear stress.

KD-302.2 Associated Mean Stress.The associatedmean stresssnm is the mean value of stress normal tothe plane subjected to the maximum alternating stressintensity.

For welded construction, the associated mean stressshall not be combined with the alternating stress inten-sity [see KD-312.4(a)].

KD-310 STRESS ANALYSIS FOR FATIGUEEVALUATION

The calculation of the number of design cycles shallbe based on a stress analysis of all fatigue-sensitivepoints.

KD-311 Loading Conditions and ResidualStresses

In this analysis, consideration shall be taken of thefollowing loadings and stresses.

KD-311.1 Residual Stresses Due to Manufacturing(a) Some manufacturing processes such as forming,

etc., introduce residual tensile stresses of unknownmagnitude. Unless these stresses are controlled by somemethod, such as postfabrication heat treatment or me-chanical overstrain processes like autofrettage, theseinitial residual stresses shall be assumed to have a peakmagnitude corresponding to the yield strength of thematerial.

(b) Manufacturing processes such as welding, heattreatment, forming, autofrettage, shrink fitting, and wirewrapping introduce residual stresses. Tensile residual

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

KD-311.1 PART KD — DESIGN REQUIREMENTS KD-312.3

stresses shall be included in the calculation of associatedmean stresses. Compressive residual stresses may alsobe included. When calculating the residual stressesintroduced by autofrettage, due account shall be takenof the influence of the Bauschinger effect (see ArticleKD-5). If any combination of operational or hydrotestloadings will produce yielding at any point, any resultingchange in the residual stress values shall be taken intoaccount.

(c) In welded construction, no credit shall be takenfor beneficial residual stresses within the weld metalor the heat-affected zone.

(d) In austenitic stainless steel construction, no creditshall be taken for beneficial residual stresses.

KD-311.2 Operating Stresses.Mean and alternatingstresses shall be calculated for all loading conditionsspecified in the User’s Design Specification. Stressconcentration factors shall be determined by analyticalor experimental techniques.

Ranges of stress intensities due to cyclic loadingsand associated mean stresses (residual plus operational)shall be calculated on the assumption of elastic behavior.If these calculations show that yielding occurs, a correc-tion shall be made. See KD-312.3.

KD-312 Calculation of Fatigue Stresses WhenPrincipal Stress Directions Do NotChange

For any case in which the directions of the principalstresses at the point being considered do not changeduring the operating cycle, the methods stated in KD-312.1 through KD-312.4 shall be used to determinethe fatigue controlling stress components.

KD-312.1 Principal Stresses.Determine the valuesof the three principal stresses at the point being investi-gated for the complete operating cycle assuming theloading and conditions described in KD-311. Thesestresses are designateds1, s2, and s3.

KD-312.2 Alternating Stress Intensities.Determinethe stress differences (maintain the proper algebraicsign for the complete operating cycle):

S12 p s1 − s2

S23 p s2 − s3

S31 p s3 − s1

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In the following, the symbolSij is used to representany one of these three differences.

Identify the algebraic largest stress differenceSij max

and the algebraic smallest differenceSij min of eachSij

during the complete operating cycle. Then the alternatingstress intensitySalt ij is determined by:

Salt ij p 0.5(Sij max − Sij min)

These three alternating stress intensities (Salt 12, Salt 23,and Salt 31) are the three ranges of shear stress thatshall be considered in a fatigue analysis. Each willhave an associated mean stress (determined below),which also influences the fatigue behavior.

KD-312.3 Associated Mean Stress(a) For welded construction, see KD-312.4(a).(b) For nonwelded construction, the associated mean

stressessnm ij shall be calculated in accordance withthe following method.

The stressessn normal to the plane of the maximumshear stress, associated with the threeSalt ij , are given by:

sn 12 p 0.5(s1 + s2)

sn 23 p 0.5(s2 + s3)

sn 31 p 0.5(s3 + s1)

In the following, the symbolsn ij is used to representany one of these normal stresses.

Identify the maximum sn ij max and the minimumsn ij min value of eachsn ij during the complete operatingcycle. Then the mean normal stressessnm ij shall becalculated by:

(1) when Sij max < Sy and Sij min > −Sy, then

snm ij p 0.5 (sn ij max + sn ij min)

(2) when Salt ij ≥ Sy, then

snm ij p 0

If neither KD-312.3(b)(1) nor (b)(2) applies, then thestress values used in this analysis shall be determinedfrom an elastic–plastic analysis (see KD-240). Alterna-tively, snm ij may be calculated as equal to 0.5(sn ij max

+ sn ij min) but not less than zero.


KD-312.4 2001 SECTION VIII — DIVISION 3 KD-322

KD-312.4 Equivalent Alternating Stress Intensity(a) For austenitic stainless steel construction, and for

welded construction within the weld metal and theheat-affected zone, effects of associated mean stresses(see Fig. KD-320.2) are incorporated in the designfatigue curve. Therefore:

Seq ij p Salt ij

(b) For nonwelded construction, the equivalent alter-nating stress intensitySeq, which is assumed to havethe same effect on fatigue as the combination of thealternating stress intensitySalt and its associated meanstresssnm, shall be calculated in accordance with theequation:

Seq ij p Salt ij1

1 − bsnm ij/S′a

where S′a is the allowable amplitude of the alternatingstress component whensnm p 0 andN p 106 cycles(see KD-321). The value ofb shall be 0.2 unlessexperimental evidence justifies another value. If thevalue of bsnm ij/S′a exceeds 0.9, limit its value to 0.9.

Using this equation, three values ofSeq ij are obtained.The largest of these three shall be used in combinationwith the design fatigue curve to establish the numberof design cycles in accordance with KD-322(c).

KD-313 Calculation of Fatigue Stresses WhenPrincipal Stress Axes Change

When the directions of the principal stresses changeduring the loading cycle, the plane carrying the maxi-mum range of shear stress cannot be easily identifiedusing equations based on principal stresses. The positionof each plane at the point of interest can be definedby two angles and a convenient set of Cartesian axes.By varying this combination of angles in increments,it is possible to determine the range of shear stress oneach plane. The largest of these shear stress ranges isequivalent to one-half of stress intensitySalt to be usedin the calculation of design cycles.

KD-320 CALCULATED NUMBER OFDESIGN CYCLES

The calculation of the number of design cyclesNf

shall be based either on design fatigue curves describedin KD-321 or on results of experimental fatigue testson components as stated in KD-1260.

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KD-321 Basis for Design Fatigue Curves

(a) The conditions and procedures of this paragraphare based on a comparison between the calculatedequivalent alternating stress intensitySeq and straincycling fatigue data. The strain cycling fatigue datahave been used to derive design fatigue curves. Thesecurves show the allowable amplitudeSa of the alternat-ing stress component (one-half of the alternating stressrange) plotted against the number of design cyclesNf,which the component is assumed to safely endurewithout failure.

(b) The design fatigue curves have been derivedfrom strain-controlled push–pull tests with zero meanstress (i.e.,snm p 0) on polished unnotched specimensin dry air. The imposed strains have been multipliedby the elastic modulus and a design margin has beenprovided so as to make the calculated equivalent stressintensity amplitude and the allowable stress amplitudedirectly comparable.Seq and Sa have the dimensionsof stress, but they do not represent a real stress whenthe elastic range is exceeded.

(c) The design fatigue curves for forged nonweldedconstruction presented in this Article have been devel-oped from fatigue tests in dry air with polished speci-mens of steels having an ultimate tensile strength inthe range of 90 ksi to 180 ksi (620 MPa to 1 242 MPa).Fatigue tests with small cylinders pressurized from theinside by oil and made of low alloy steels having anultimate tensile strength in the range of 130 ksi to 180ksi (896 MPa to 1 242 MPa) have been used to confirmthe validity of these curves for carbon or low alloyforgings with machined surfaces. For design fatiguecurves, see Fig. KD-320.1 for forged nonwelded con-struction, Fig. KD-320.2 for welded construction, andFig. KD-320.3 for austenitic stainless steel construction.

(d) The design fatigue curves are not applicable inthe presence of aggressive environments. For conditionsnot covered by these design fatigue curves, the Manufac-turer shall provide supplementary fatigue data.

KD-322 Use of Design Fatigue Curve

(a) Figure KD-320.1 shall be used for forged non-welded parts with machined surfaces made of carbonor low alloy steels having a specified minimum valueof the ultimate tensile strengthSu greater than 90ksi. The curves are applicable for an average surfaceroughness of 10Ra min. in fatigue-sensitive areas.Lower quality surface finish will influence fatigue. Thisinfluence is considered by a factorKr (see Fig. KD-320.4), which shall be combined withSeq as specified


PART KD — DESIGN REQUIREMENTS Fig. KD-320.1

FIG

.K

D-3

20.1

DE

SIG

NF

AT

IGU

EC

UR

VE

SS e

qp

f(N

f)F

OR

NO

NW

EL

DE

DM

AC

HIN

ED

PA

RT

SM

AD

EO

FF

OR

GE

DC

AR

BO

NO

RL

OW

AL

LO

YS

TE

EL

S

55


Fig. KD-320.2 2001 SECTION VIII — DIVISION 3

FIG

.K

D-3

20.2

DE

SIG

NF

AT

IGU

EC

UR

VE

S eq

pf(

Nf)

FO

RW

EL

DE

DP

AR

TS

MA

DE

OF

CA

RB

ON

OR

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WA

LL

OY

ST

EE

LS

56


PART KD — DESIGN REQUIREMENTS Fig. KD-320.3

FIG

.K

D-3

20.3

DE

SIG

NF

AT

IGU

EC

UR

VE

FO

RA

US

TE

NIT

ICS

TA

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ES

SS

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MP

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AT

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ES

NO

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DIN

G80

0°F

57


Table KD-320.1 2001 SECTION VIII — DIVISION 3

TABLE KD-320.1TABULATED VALUES OF Seq, ksi, FROM FIGURES INDICATED

Number of Design Operating Cycles Nf

Figure Curve 5E1 1E2 2E2 5E2 1E3 2E3 5E3 1E4 2E4 5E4 1E5 2E5 5E5 1E6 2E6

320.1 UTS 90 ksi 311 226 164 113 89 72 57 49 43 34 29 25 21 19 17320.1 UTS 125 ksi 317 233 171 121 98 82 68 61 49 39 34 31 28 26 24320.2 Welded 275 205 155 105 83 64 48 38 31 24 20 16.5 13.5 12.5 . . .320.3 Austenitic 345 261 201 148 119 97 76 64 56 46 41 36 31 28 . . .

stainlesssteels

GENERAL NOTES:(a) All notes on the referenced figures apply to these data.(b) Number of design cycles indicated shall be read as follows: 1EJ p 1 × 10J, e.g., 5E2 p 5 × 102 or 500 cycles.(c) Interpolation between tabular values is permissible based upon data representation by straight lines on a log–log plot. Accordingly, for Si

> S > Sj,

NNi

p 1Nj

Ni2[log(S

i/S)/log(S

i/S

j)]

whereS, Si, Sj p values of Sa

N, Ni, Nj p corresponding calculated number of design cycles from design fatigue dataFor example, from the data above, use the interpolation formula above to find the calculated number of design cycles N for Seq p 50.0

ksi when UTS ≥ 125 ksi on Fig. KD-320.1:

N10,000

p 120,00010,0002

[log(61/50)/log(61/49)]

N p 18,800 cycles

(d) Equations for number of design operating cycles:(1) Fig. KD-320.1, UTS p 90 ksi

Seq ≥ 42.6 ksi ln(N) p 15.433 − 2.0301 ln(Seq) + 1036.035 ln(Seq)/S2eq

Seq < 42.6 ksi 1/N p 2.127E−05 + (7.529E−10)S3eq − (8.636E−06)ln(Seq)

(2) Fig. KD-320.1, UTS p 125–175 ksiSeq ≥ 60.6 ksi 1/N p 0.00122 − (7.852E−05)Seq + (7.703E−06)S1.5

eqSeq < 60.6 ksi N0.5 p (7.8628E−05 + 0.003212Seq + 0.0936S2

eq)/[1 − 0.08599Seq + 0.001816S2eq +

(4.05774E−06)S3eq]

(3) Fig. KD-320.2, weldedSeq ≥ 38 ksi 1/N p −0.0007125 + (4.4692E−08)(S2

eq)ln(Seq) + 0.003561/S0.5eq

Seq < 38 ksi ln(N) p (18.0353 − 1.3663Seq − 0.01549S2eq)/(1 − 0.04031Seq − 0.003854S2

eq)

(4) Fig. KD-320.3, austenitic stainless steelsSeq ≥ 55.7 ksi ln(N) p (0.0303 − 0.7531Seq − 0.0001968S2

eq)/(1 − 0.0723Seq − 0.0004075S2eq)

Seq < 55.7 ksi ln(N)p (0.0002445 + 0.001656Seq − 0.03416S2eq)/[1 − 0.06062Seq − 0.000429S2

eq − (4.049E−05)S3

eq]

(e) Equations shall not be used outside of the cycle range given in the Table.

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KD-322 PART KD — DESIGN REQUIREMENTS KD-330

FIG. KD-320.4 ROUGHNESS FACTOR Kr VERSUS SURFACE FINISH Ra min. AA

in KD-322(d) when determining the calculated numberof design cyclesNf.

(b) Figure KD-320.2 shall be used for those areasof the vessel that contain butt welded joints groundflush. The influence of the surface roughness is includedin the curve, i.e.,Kr p 1.0; therefore, a surfaceroughness factor need not be applied. For other typesof welded joints, not ground flush but permitted bythis Division, appropriate stress concentration factorsshall be determined and used.

(c) Figure KD-320.3 shall be used for forged non-welded parts with machined surfaces made of austeniticstainless steels. The influence of the surface roughnessis included in the curve, i.e.,Kr p 1.0; therefore, asurface roughness factor need not be applied.

(d) When the operational cycle being considered isthe only one that produces significant fluctuatingstresses, the calculated number of design cyclesNf isdetermined as follows.

(1) Identify the applicable fatigue curve for thematerial as explained in KD-322(a) and (b).

(2) Multiply Seq by the ratio of the modulus ofelasticity given on the design fatigue curve to the valueused in the analysis.

(3) Enter the curve from the ordinate axis at thevalue:

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Sa p Kr Seq

(4) Read the corresponding number of cycles onthe abscissa. This is the calculated number of designcycles Nf.

KD-330 CALCULATED CUMULATIVEEFFECT NUMBER OF DESIGNCYCLES

If there are two or more types of stress cycleswhich produce significant stresses, the alternating stressintensity and the associated mean stress shall be calcu-lated for each type of stress cycle. The cumulativeeffect of all of the stress cycles shall be evaluatedusing a linear damage relationship as specified in KD-330(a) through (f).

(a) Calculate the number of times each type of stresscycle of type 1, 2, 3, etc., will be repeated during aspecific design service life periodL. It is recommendedthat L be based on the design serviceLd as specifiedin the User’s Design Specification; designate thesenumbersn1, n2, n3, etc., or generallyni .

(b) For each type of stress cycle, determineSeq bythe procedures given in KD-312.4. Designate thesequantitiesSeq 1, Seq 2, Seq 3, etc., or generallySeq i.


KD-330 2001 SECTION VIII — DIVISION 3 KD-330

(c) For each valueSeq i, use the applicable designfatigue curve to determine the maximum number ofdesign repetitionsNi if this type of cycle were theonly one acting. Designate these asN1, N2, N3, etc.,or generallyNi .

(d) For each type of stress cycle, calculate the usagefactor Ui p ni /Ni .

(e) Calculate the cumulative usage factor from:

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U p oi

ip1

ni

Ni, or p U1 + U2 . . .

The cumulative usage factorU shall not exceed 1.0.(f) Calculate the design serviceLd using the equation:

Ld p L/U


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ASME SEC VIII D3 PART KD-3.pdf