SEC VIII D3 ART KD-3

7/29/2019 SEC VIII D3 ART KD-3

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ARTICLE KD-3

FATIGUE EVALUATION

KD-300 SCOPE

This Article presents a traditional fatigue analysis

design approach. In accordance with KD-140, if it can

be shown that the vessel will fail in a leak-before-

burst mode, then the number of design cycles shall be

calculated in accordance with either Article KD-3 or

Article KD-4. If a leak-before-burst mode of failure

cannot 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 pressure

vessels and components. While cracks often initiate at

the bore, cracks may initiate at outside surfaces or at

layer interfaces for autofrettaged and layered vessels.

In all cases, areas of stress concentrations are a particular

concern. Fatigue-sensitive points shall be identified and

a fatigue analysis made for each point. The result of

the fatigue analysis will be a calculated number of

design cycles Nf for each type of operating cycle, anda calculated cumulative effect number of design cycles

when more than one type of operating cycle exists.

The resistance to fatigue of a component shall be

based on the design fatigue curves for the materials

used. For design fatigue curves, see Fig. KD-320.1 for

forged nonwelded construction and Fig. KD-320.2 for

welded construction.

In some cases it may be convenient or necessary to

obtain experimental fatigue data for a component itself

rather than for small specimens of the material (see

KD-1260). If there are two or more types of stress

cycles which produce significant stresses, their cumula-

tive effect shall be evaluated by calculating for each

type of stress cycle the usage factors U1, U2, U3, etc.,

and the cumulative usage factor U per KD-330. The

cumulative usage factor U shall not exceed 1.0.

KD-302 Theory

The theory used in this Article postulates that fatigue

at any point is controlled by the alternating stress

52

intensity Salt and the associated mean stress nm normal

to the plane of Salt. They are combined to define the

equivalent alternating stress intensity Seq, which is used

with the design fatigue curves to establish the number

of design cycles Nf.

KD-302.1 Alternating Stress Intensity. The alternat-

ing stress intensity Salt represents the maximum range

of shear stress.

KD-302.2 Associated Mean Stress. The associated

mean stress nm is the mean value of stress normal to

the plane subjected to the maximum alternating stress

intensity.

For welded construction, the associated mean stress

shall not be combined with the alternating stress inten-

sity [see KD-312.4(a)].

KD-310 STRESS ANALYSIS FOR FATIGUE

EVALUATION

The calculation of the number of design cycles shall

be based on a stress analysis of all fatigue-sensitive

points.

KD-311 Loading Conditions and Residual

Stresses

In this analysis, consideration shall be taken of the

following loadings and stresses.

KD-311.1 Residual Stresses Due to Manufacturing

(a) Some manufacturing processes such as forming,

etc., introduce residual tensile stresses of unknown

magnitude. Unless these stresses are controlled by some

method, such as postfabrication heat treatment or me-

chanical overstrain processes like autofrettage, these

initial residual stresses shall be assumed to have a peak

magnitude corresponding to the yield strength of the

material.

(b) Manufacturing processes such as welding, heat

treatment, forming, autofrettage, shrink fitting, and wire

wrapping introduce residual stresses. Tensile residual

YRIGHT American Society of Mechanical Engineersensed by Information Handling Services


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KD-311.1 PART KD DESIGN REQUIREMENTS KD-312.3

stresses shall be included in the calculation of associated

mean stresses. Compressive residual stresses may also

be included. When calculating the residual stresses

introduced by autofrettage, due account shall be taken

of the influence of the Bauschinger effect (see Article

KD-5). If any combination of operational or hydrotestloadings will produce yielding at any point, any resulting

change in the residual stress values shall be taken into

account.

(c) In welded construction, no credit shall be taken

for beneficial residual stresses within the weld metal

or the heat-affected zone.

(d) In austenitic stainless steel construction, no credit

shall be taken for beneficial residual stresses.

KD-311.2 Operating Stresses. Mean and alternating

stresses shall be calculated for all loading conditions

specified in the Users Design Specification. Stress

concentration factors shall be determined by analyticalor experimental techniques.

Ranges of stress intensities due to cyclic loadings

and 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 When

Principal Stress Directions Do Not

Change

For any case in which the directions of the principal

stresses 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 determine

the fatigue controlling stress components.

KD-312.1 Principal Stresses. Determine the values

of the three principal stresses at the point being investi-

gated for the complete operating cycle assuming the

loading and conditions described in KD-311. These

stresses are designated 1 , 2 , and 3 .

KD-312.2 Alternating Stress Intensities. Determine

the stress differences (maintain the proper algebraic

sign for the complete operating cycle):

S12 p 1 2

S23 p 2 3

S31 p 3 1

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In the following, the symbol Sij is used to represent

any one of these three differences.

Identify the algebraic largest stress difference Sij maxand the algebraic smallest difference Sij min of each Sijduring the complete operating cycle. Then the alternating

stress intensity Salt 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 that

shall be considered in a fatigue analysis. Each will

have 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

stresses nm ij shall be calculated in accordance withthe following method.

The stresses n normal to the plane of the maximum

shear stress, associated with the three Salt ij, are given by:

n 12 p 0.5(1 + 2)

n 23 p 0.5(2 + 3)

n 31p

0.5(3 + 1)

In the following, the symbol n ij is used to represent

any one of these normal stresses.

Identify the maximum n ij max and the minimum

n ij min value of each n ij during the complete operating

cycle. Then the mean normal stresses nm ij shall be

calculated by:

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

nm ij p 0.5 (n ij max + n ij min)

(2) when Salt ij Sy, then

nm ij p 0

If neither KD-312.3(b)(1) nor (b)(2) applies, then the

stress values used in this analysis shall be determined

from an elasticplastic analysis (see KD-240). Alterna-

tively, nm ij may be calculated as equal to 0.5(n ij max+ n ij min) but not less than zero.



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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 the

heat-affected zone, effects of associated mean stresses

(see Fig. KD-320.2) are incorporated in the design

fatigue curve. Therefore:

Seq ij p Salt ij

(b) For nonwelded construction, the equivalent alter-

nating stress intensity Seq, which is assumed to have

the same effect on fatigue as the combination of the

alternating stress intensity Salt and its associated mean

stress nm, shall be calculated in accordance with the

equation:

Seq ij p Salt ij1

1 nm ij

/Sa

where Sa is the allowable amplitude of the alternating

stress component when nm p 0 and Np 106 cycles

(see KD-321). The value of shall be 0.2 unless

experimental evidence justifies another value. If the

value of nm ij/Sa exceeds 0.9, limit its value to 0.9.

Using this equation, three values of Seq ij are obtained.

The largest of these three shall be used in combination

with the design fatigue curve to establish the number

of 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 change

during the loading cycle, the plane carrying the maxi-

mum range of shear stress cannot be easily identified

using equations based on principal stresses. The position

of each plane at the point of interest can be defined

by 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 on

each plane. The largest of these shear stress ranges is

equivalent to one-half of stress intensity Salt to be used

in the calculation of design cycles.

KD-320 CALCULATED NUMBER OF

DESIGN CYCLES

The calculation of the number of design cycles Nfshall be based either on design fatigue curves described

in KD-321 or on results of experimental fatigue tests

on components as stated in KD-1260.

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KD-321 Basis for Design Fatigue Curves

(a) The conditions and procedures of this paragraph

are based on a comparison between the calculated

equivalent alternating stress intensity Seq and strain

cycling fatigue data. The strain cycling fatigue data

have been used to derive design fatigue curves. Thesecurves show the allowable amplitude Sa of the alternat-

ing stress component (one-half of the alternating stress

range) plotted against the number of design cycles Nf,

which the component is assumed to safely endure

without failure.

(b) The design fatigue curves have been derived

from strain-controlled pushpull tests with zero mean

stress (i.e., nm p 0) on polished unnotched specimens

in dry air. The imposed strains have been multiplied

by the elastic modulus and a design margin has been

provided so as to make the calculated equivalent stress

intensity amplitude and the allowable stress amplitude

directly comparable. Seq and Sa have the dimensions

of stress, but they do not represent a real stress when

the elastic range is exceeded.

(c) The design fatigue curves for forged nonwelded

construction 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 in

the range of 90 ksi to 180 ksi (620 MPa to 1 242 MPa).

Fatigue tests with small cylinders pressurized from the

inside by oil and made of low alloy steels having an

ultimate tensile strength in the range of 130 ksi to 180

ksi (896 MPa to 1 242 MPa) have been used to confirm

the validity of these curves for carbon or low alloyforgings with machined surfaces. For design fatigue

curves, see Fig. KD-320.1 for forged nonwelded con-

struction, Fig. KD-320.2 for welded construction, and

Fig. KD-320.3 for austenitic stainless steel construction.

(d) The design fatigue curves are not applicable in

the presence of aggressive environments. For conditions

not 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 carbon

or low alloy steels having a specified minimum value

of the ultimate tensile strength Su greater than 90

ksi. The curves are applicable for an average surface

roughness of 10 Ra in. in fatigue-sensitive areas.

Lower quality surface finish will influence fatigue. This

influence is considered by a factor Kr (see Fig. KD-

320.4), which shall be combined with Seq as specified



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PART KD DESIGN REQUIREMENTS Fig. KD-320.1

FIG.

KD-32

0.1

DESIGNFATIGUECURVESSeq

p

f(Nf)FORNONWELDEDMACHINE

DPARTSMADEOFFORGEDCARBO

NOR

LOW

ALLOYSTEELS

55



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Fig. KD-320.2 2001 SECTION VIII DIVISION 3

FIG.

KD-320.2

DESIGNFATIGUECURVESeqp

f(Nf)FORWELDEDPARTSMAD

EOFCARBONORLOW

ALLOYSTEELS

56



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PART KD DESIGN REQUIREMENTS Fig. KD-320.3

FIG.

KD-320.3

DESIGNFATIGUECURVEFORAUSTENITICSTAINLESSSTEELSFORTEMPERATURESNOTEXCEEDING

800F

57



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Table KD-320.1 2001 SECTION VIII DIVISION 3

TABLE KD-320.1

TABULATED VALUES OF Seq, ksi, FROM FIGURES INDICATEDNumber 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 17

320.1 UTS 125 ksi 317 233 171 121 98 82 68 61 49 39 34 31 28 26 24

320.2 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 . . .

stainless

steels

GENERAL NOTES:(a) All notes on the referenced figures apply to these data.(b) Number of design cycles indicated shall be read as follows: 1EJp 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 loglog plot. Accordingly, for Si

> S> Sj,

N

Nip NjNi

[log(Si

/S)/log(Si

/Sj

)]

whereS, Si, Sjp values of Sa

N, Ni, Njp 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 Seqp 50.0

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

N

10,000p 20,00010,000

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

Np 18,800 cycles

(d) Equations for number of design operating cycles:

(1) Fig. KD-320.1, UTSp 90 ksiSeq 42.6 ksi ln(N) p 15.433 2.0301 ln(Seq) + 1036.035 ln(Seq)/S

2eq

Seq < 42.6 ksi 1/ Np 2.127E05 + (7.529E10)S3eq (8.636E06)ln(Seq)

(2) Fig. KD-320.1, UTSp 125175 ksiSeq 60.6 ksi 1/ Np 0.00122 (7.852E05)Seq + (7.703E06)S

1.5eq

Seq < 60.6 ksi N0.5p (7.8628E05 + 0.003212Seq + 0.0936S

2eq)/[1 0.08599Seq + 0.001816S

2eq +

(4.05774E06)S3eq]

(3) Fig. KD-320.2, weldedSeq 38 ksi 1/ Np 0.0007125 + (4.4692E08)(S

2eq)ln(Seq) + 0.003561/S

0.5eq

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

2eq)

(4) Fig. KD-320.3, austenitic stainless steels

Seq 55.7 ksi ln(N) p (0.0303 0.7531Seq 0.0001968S2eq)/(1 0.0723Seq 0.0004075S2eq)Seq < 55.7 ksi ln(N)p (0.0002445 + 0.001656Seq 0.03416S

2eq)/[1 0.06062Seq 0.000429S

2eq (4.049E05)

S3eq]

(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 Rain. AA

in KD-322(d) when determining the calculated number

of design cycles Nf.

(b) Figure KD-320.2 shall be used for those areas

of the vessel that contain butt welded joints ground

flush. The influence of the surface roughness is includedin the curve, i.e., Kr p 1.0; therefore, a surface

roughness factor need not be applied. For other types

of welded joints, not ground flush but permitted by

this Division, appropriate stress concentration factors

shall be determined and used.

(c) Figure KD-320.3 shall be used for forged non-

welded parts with machined surfaces made of austenitic

stainless steels. The influence of the surface roughness

is included in the curve, i.e., Kr p 1.0; therefore, a

surface roughness factor need not be applied.

(d) When the operational cycle being considered is

the only one that produces significant fluctuating

stresses, the calculated number of design cycles Nf isdetermined as follows.

(1) Identify the applicable fatigue curve for the

material as explained in KD-322(a) and (b).

(2) Multiply Seq by the ratio of the modulus of

elasticity given on the design fatigue curve to the value

used in the analysis.

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

value:

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Sa p KrSeq

(4) Read the corresponding number of cycles on

the abscissa. This is the calculated number of design

cycles Nf

.

KD-330 CALCULATED CUMULATIVE

EFFECT NUMBER OF DESIGN

CYCLES

If there are two or more types of stress cycles

which produce significant stresses, the alternating stress

intensity and the associated mean stress shall be calcu-

lated for each type of stress cycle. The cumulative

effect of all of the stress cycles shall be evaluated

using a linear damage relationship as specified in KD-

330(a) through (f).

(a) Calculate the number of times each type of stress

cycle of type 1, 2, 3, etc., will be repeated during a

specific design service life period L. It is recommended

that L be based on the design service Ld as specified

in the Users Design Specification; designate these

numbers n1, n2, n3, etc., or generally ni .

(b) For each type of stress cycle, determine Seq by

the procedures given in KD-312.4. Designate these

quantities Seq 1, Seq 2, Seq 3, etc., or generally Seq i .



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KD-330 2001 SECTION VIII DIVISION 3 KD-330

(c) For each value Seq i, use the applicable design

fatigue curve to determine the maximum number of

design repetitions Ni if this type of cycle were the

only one acting. Designate these as N1, N2, N3, etc.,

or generally Ni .

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

(e) Calculate the cumulative usage factor from:

60

Upi

ip1

niNi

, or p U1 + U2 . . .

The cumulative usage factor U shall not exceed 1.0.

(f) Calculate the design service Ld using the equation:

Ldp L /U

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SEC VIII D3 ART KD-3