203192429-apendice-5-asme-viii-2.pdf

APPENDIX 5 — MANDATORY DESIGN BASED ON FATIGUE ANALYSIS ARTICLE 5-1 5-100

ANALYSIS FOR CYCLIC OPERATION

number of cycles. This stress amplitude is calculated on the assumption of elastic behavior and hence has the dimensions of stress, but it does not represent a real stress when the elastic range is exceeded. The fatigue curves are obtained from uniaxial strain cycling data in which the imposed strains have been multiplied by the elastic modulus and a design margin has been provided, so as to make the calculated stress intensity and amplitude and the allowable stress amplitude directly comparable. As an exception to the use of strain controlled test data, Fig. 5-110.2.2 curves B and C are based on load controlled fatigue data. The curves have been adjusted, where necessary, to include the maximum effects of mean stress, which is the condition where the stress fluctuates about a mean value which is different from zero. As a consequence of this procedure, it is essential that the requirements of 4-135 and 4137 be satisfied at all times, with transient stresses included, and that the calculated value of the alternating stress intensity be proportional to the actual strain amplitude. To evaluate the effect of alternating stresses of varying amplitudes, a linear damage relation is assumed in 5-110.3(e).

The suitability of a vessel component for specified operating conditions involving cyclic application of loads and thermal conditions shall be determined by the methods described herein, except that the suitability of high strength bolts shall be determined by the methods of 5-120 and the possibility of thermal stress ratchet shall be investigated in accordance with 5-130. If the specified operation of the vessel meets all of the conditions of AD-160, no analysis for cyclic operation is required and it may be assumed that the peak stress limit discussed in 4-135 has been satisfied by compliance with the applicable requirements for materials, design, fabrication, testing, and inspection of this Division. If the operation does not meet all the conditions of AD160, a fatigue analysis shall be made in accordance with 5-110 or a fatigue test shall be made in accordance with 6-170. 5-101

Allowable Amplitude of Alternating Stresses

The conditions and procedures of AD-160 and 5-110 are based on a comparison of peak stresses with strain cycling fatigue data. The strain cycling fatigue data are represented by the design fatigue strength curves of Figs. 5-110.1, 5-110.2.1, 5-110.2.2, 5-110.2.3, 5110.3, and 5-110.4.1 These curves show the allowable amplitude Sa of the alternating stress component (onehalf of the alternating stress range) plotted against the

5-102

Loadings to Be Considered

The loadings to be considered shall include those loads that are due to testing of the vessel when such testing is in addition to that required by this Division.

5-110 1 The

tests on which the design curves are based did not include tests at temperatures in the creep range or in the presence of unusually corrosive environments, either of which might accelerate fatigue failure. Therefore, these curves are not applicable at operating temperatures for which creep is a significant factor. In addition, the designer shall evaluate separately any effects on fatigue life which might result from an unusually corrosive environment.

DESIGN FOR CYCLIC LOADING

5-110.1 Determination of Vessel’s Ability to Withstand Cyclic Loading. If the specified operation of the vessel does not meet the condition of AD-160, the ability of the vessel to withstand the specified cyclic operation without fatigue failure shall be determined 395

5-110.1

1998 SECTION VIII — DIVISION 2

as provided hereinafter. The determination shall be made on the basis of the stresses at a point of the vessel and the allowable stress cycles shall be adequate for the specified operation at every point. Only the stresses due to the specified cycle of operation need be considered; stresses produced by any load or thermal condition which does not vary during the cycle need not be considered, since they are mean stresses and the maximum possible effect of mean stress is included in the fatigue design curves.

5-110.3

stress cycle, it is necessary to use the following more general procedure. (1) Consider the values of the six stress components st , sl , sr , tlt , tlr , and trt versus time for the complete stress cycle. (2) Choose a point in time when the conditions are one of the extremes for the cycle (either maximum or minimum, algebraically) and identify the stress components at this time by the subscript i. In most cases it will be possible to choose at least one time during the cycle when the conditions are known to be extreme. In some cases it may be necessary to try different points in time to find the one which results in the largest value of alternating stress intensity. (3) Subtract each of the six stress components sti , sli, etc., from the corresponding stress components st , sl, etc., at each point in time during the cycle and call the resulting components s ′t , s ′l, etc. (4) At each point in time during the cycle, calculate the principal stresses s ′1, s ′2, and s ′3 derived from the six stress components s ′t , s ′l, etc. Note that the directions of the principal stresses may change during the cycle, but each principal stress retains its identity as it rotates. (5) Determine the stress differences,

5-110.2 Significance of Compliance With Requirements for Cyclic Loading. Compliance with these requirements means only that the vessel is suitable from the standpoint of possible fatigue failure; complete suitability for the specified operation is also dependent on meeting the general stress limits of 4-130 and any applicable special stress limits of 5-130. 5-110.3 Cyclic Loading Design Procedure. Subparagraphs 5-110.3(a) and 5-110.3(b) apply to the determination of primary plus secondary stress intensity range (see 4-134) and peak stress intensity range (see 4-135). (a) When Principal Stress Direction Does Not Change. For any case in which the directions of the principal stresses at the point being considered do not change during the cycle, the following steps shall be followed to determine the alternating stress intensity. (1) Principal Stresses. Consider the values of the three principal stresses at the point versus time for the complete stress cycle. These are designated as s1, s2, and s3 for later identification. (2) Stress Differences. Determine the stress differences

S″12 p s ′1 − s ′2

S″23 p s ′2 − s ′3

S″31 p s ′3 − s ′1

S12 p s1 − s2

versus time for the complete cycle and find the largest absolute magnitude of any stress difference at any time. Call this value Srij. (c) When evaluating the limits for the primary plus secondary stress intensity range, Srij is compared to the 3Sm limit (see 4-134). (d) The alternating stress intensity Salt is one half the value of Srij. (e) Design Fatigue Curves. Figures 5-110.1, 5110.2.1, 5-110.2.2, 5-110.3, and 5-110.4 contain applicable design fatigue curves for some of the materials permitted by this Division [see AM-100(c)]. When more than one curve is presented for a given material, the applicability of each is identified. Where curves for various strength levels of a material are given, linear interpolation may be used for intermediate strength levels of these materials. As used herein, the

S23 p s2 − s3 S31 p s3 − s1

versus time for the complete cycle. In what follows, the symbol Sij is used to represent any one of three stress differences. (3) Stress Intensity Range. Determine the extremes of the range through which each stress difference Sij fluctuates, and find the absolute magnitude of this range for each Sij. Call the largest absolute magnitude of these values Srij. (b) When Principal Stress Direction Changes. For any case in which the directions of the principal stresses at the point being considered do change during the 396

FIG. 5-110.1 DESIGN FATIGUE CURVES FOR CARBON, LOW ALLOY, SERIES 4XX, HIGH ALLOY STEELS AND HIGH TENSILE STEELS FOR TEMPERATURES NOT EXCEEDING 700°F

APPENDIX 5 — MANDATORY

397

Fig. 5-110.1

5-110.3

1998 SECTION VIII — DIVISION 2

5-110.3

TABLE 5-110.1 TABULATED VALUES OF Sa , ksi, FROM FIGURES INDICATED Number of Cycles1 Figure

Curve

1E1

2E1

5-110.1 5-110.1 5-110.2.1 5-110.2.2 5-110.3 5-110.3 5-110.3 5-110.4 5-120.1 5-120.1

UTS 115–130 ksi UTS ≤ 80 ksi ... ... Sy p 18.0 ksi Sy p 30.0 ksi Sy p 45.0 ksi ... MNS3 ≤ 2.7Sm MNS3 p 3Sm

420 580 708

320 410 512

260 260 260 708 1150 1150

5E1

230 275 345 See Table 5-110.2 190 125 190 125 190 125 512 345 760 450 760 450

1E2

2E2

5E2

8.5E22

175 205 261

135 155 201

100 105 148

... ... ...

95 95 95 261 320 300

73 73 73 201 225 205

52 52 52 148 143 122

... ... 46 ... ... ...

GENERAL NOTES: (a) All notes in the referenced figures apply to these data. (b) Interpolation between tabular values is permissible based upon data representation by straight lines on a log-log plot. Accordingly, for Si > S > Sj , [log (Si /S)] / log (Si /Sj )

1 2

N Nj p Ni Ni

where S, Si , Sj p values of Sa N, Ni , Nj p corresponding number of cycles from design fatigue data Example: From data in the table, use the interpolation formula above to find the number of cycles N for Sa p 53.5 ksi when UTS ≤ 80 ksi in Fig. 5-110.1.

1

[log (64/53.5)] / log (64/48)

2

N 5000 p 2000 2000

N p 3540 cycles NOTES: (1) Number of cycles indicated shall be read as follows: I EJ p I × 10J, e.g., 5E2 p 5 × 102 or 500. (2) These data points are included to provide accurate representation of curves at branches or cusps. (3) Maximum nominal stress.

strength level is the specified minimum room temperature value. The design fatigue curves are defined over a cyclic range of 10 to 106 cycles, except that for nickel– chromium–molybdenum–iron alloy, a cyclic range of 10 to 108 cycles is provided in Fig. 5-110.4 and that for series 3XX high alloy steels, nickel–chromium–iron alloy, nickel–iron–chromium alloy, and nickel–copper alloy, the design fatigue curves are extended to 1011 cycles in Fig. 5-110.2.2. Criteria for the use of the latter curves are given in Fig. 5-110.2.2 and are also presented graphically by the flowchart given in Fig. 5110.2.3. (f) Use of Design Fatigue Curve. Multiply Salt [as determined in (a) or (b)] by the ratio of the modulus of elasticity given on the design fatigue curve to the value used in the analysis. Enter the applicable design fatigue curve at this value on the ordinate axis and

find the corresponding number of cycles on the axis of abscissas. If the operational cycle being considered is the only one which produces significant fluctuating stresses, this is the allowable number of cycles. (g) Cumulative Damage. If there are two or more types of stress cycle which produce significant stresses, their cumulative effect shall be evaluated as given below. (1) Designate the specified number of times each type of stress cycle of types 1, 2, 3, etc., will be repeated during the life of the vessel as n1 , n2 , n3 , etc., respectively. In determining n1 , n2 , n3 , etc., consideration shall be given to the superposition of cycles of various origins which produce a total stress difference range greater than the stress difference ranges of the individual cycles. For example, if one type of stress cycle produces 1000 cycles of a stress difference varia398

5-110.3

APPENDIX 5 — MANDATORY

5-112

TABLE 5-110.1 TABULATED VALUES OF Sa , ksi, FROM FIGURES INDICATED Number of Cycles1 1.2E42

2E4

5E4

1E5

2E5

5E5

1E6

2E6

5E6

1E7

2E7

5E7

1E8

44 38 64

43 ... ...

36 31 55.5

29 23 46.3

26 20 40.8

24 16.5 35.9

22 13.5 31.0

20 12.5 28.3

... ... ...

... ... ...

... ... ...

... ... ...

... ... ...

... ... ...

24.5 24.5 12 64 34 22.5

... ... ... ... ... ...

21 19.5 9.6 56 27 15

17 15 7.7 46.3 22 10.5

15 13 6.7 40.8 19 8.4

13.5 11.5 6.0 35.9 17 7.1

12.5 9.5 5.2 26.0 15 6

12.0 9.0 5.0 20.7 13.5 5.3

... ... ... 18.7 ... ...

... ... ... 17.0 ... ...

... ... ... 16.2 ... ...

... ... ... 15.7 ... ...

... ... ... 15.3 ... ...

... ... ... 15.0 ... ...

1E3

2E3

5E3

1E4

78 83 119

62 64 97

49 48 76

44 44 39 119 100 81

36 36 24.5 97 71 55

28.5 28.5 15.5 76 45 33

tion from zero to +60,000 psi and another type of stress cycle produces 10,000 cycles of a stress difference variation from zero to −50,000 psi, the two types of cycle to be considered are defined by the following parameters: Type 1 cycle:

U3 p n3 /N3

etc. (5) Calculate the cumulative usage factor U from U p U 1 + U2 + U3 + . . .

n1 p 1000

etc. (6) The cumulative usage factor U shall not exceed 1.0.

Salt 1 p (60,000 + 50,000) /2 p 55,000 psi

Type 2 cycle: 5-111

n2 p 9000

Local Structural Discontinuities

These effects shall be evaluated for all conditions using stress concentration factors determined from theoretical, experimental, or photoelastic studies or finite element stress analysis techniques. Experimentally determined fatigue strength reduction factors may be used when determined in accordance with the procedures of 6-180, in lieu of specific values when provided in this Division and except for high strength alloy steel bolts and studs for which the requirements of 5-110 shall apply when using the design fatigue curve of Fig. 5-120.1. Except for the case of crack-like defects, no fatigue strength reduction factor greater than five need be used.

Salt 2 p (50,000 + 0) /2 p 25,000 psi

(2) For each type of stress cycle, determine the alternating stress intensity Salt by the procedures of (a) or (b) above. Call these quantities Salt 1, Salt 2, Salt 3, etc. (3) For each value Salt 1, Salt 2, Salt 3, etc., use the applicable design fatigue curve to determine the maximum number of repetitions which would be allowable if this type of cycle were the only one acting. Call these values N1 , N2 , N3 , etc. (4) For each type of stress cycle, calculate the usage factors U1 , U2 , U3 , etc., from U1 p n1 /N1

5-112

U2 p n2 /N2

Fillet welds shall not be used in vessels for joints of Categories A, B, C, or D (see Fig. AD-400.1), 399

Fillet Welds

FIG. 5-110.2.1 DESIGN FATIGUE CURVE FOR SERIES 3XX HIGH ALLOY STEELS, NICKEL–CHROMIUM–IRON ALLOY, NICKEL–IRON–CHROMIUM ALLOY, AND NICKEL–COPPER ALLOY FOR TEMPERATURES NOT EXCEEDING 800°F AND Sa > 28.2 ksi (USE FIG. 5-110.2.2 FOR Sa ≤ 28.2 ksi)

Fig. 5-110.2.1 1998 SECTION VIII — DIVISION 2

400

APPENDIX 5 — MANDATORY

Fig. 5-110.2.2

FIG. 5-110.2.2 DESIGN FATIGUE CURVE FOR SERIES 3XX HIGH ALLOY STEELS, NICKEL–CHROMIUM–IRON ALLOY, NICKEL–IRON–CHROMIUM ALLOY, AND NICKEL–COPPER ALLOY FOR TEMPERATURES NOT EXCEEDING 800°F AND Sa ≤ 28.2 ksi (USE FIG. 5-110.2.1 FOR Sa > 28.2 ksi)

401

5-112

1998 SECTION VIII — DIVISION 2

5-120

FIG. 5-110.2.3 GRAPHICAL PRESENTATION OF CRITERIA FOR USE OF CURVES IN FIG. 5-110.2.2

except as permitted for joints of Category C for slipon flanges (see AD-413 and AD-711.1) and for joints of Category D as permitted in Article D-6. Fillet welds may be used for attachments to pressure vessels using one-half the stress limits of 4-131 through 4-134 for primary and secondary stresses. Evaluation for cyclic loading shall be made in accordance with Appendix 5 using a fatigue strength reduction factor of four and shall include consideration of temperature differences between the vessel and the attachment and expansion

or contraction of the vessel produced by internal or external pressure.

5-120

FATIGUE ANALYSIS OF BOLTS

Unless the vessel on which they are installed meets all the conditions of AD-160 and thus requires no fatigue analysis, the suitability of bolts for cyclic operation shall 402

5-120

APPENDIX 5 — MANDATORY TABLE 5-110.2 TABULATED VALUES OF Sa, ksi, FROM FIG. 5-110.2.2

Number of Cycles [Note (1)]

Curve A

Curve B

Curve C

1E6 2E6 5E6 1E7 2E7

28.2 26.9 25.7 25.1 24.7

28.2 22.8 19.8 18.5 17.7

28.2 22.8 18.4 16.4 15.2

5E7 1E8 1E9 1E10 1E11

24.3 24.1 23.9 23.8 23.7

17.2 17.0 16.8 16.6 16.5

14.3 14.1 13.9 13.7 13.6

5-130

(4) fillet radii at the end of the shank shall be such that the ratio of fillet radius to shank diameter is not less than 0.060; (5) the fatigue strength reduction factor used in the fatigue evaluation shall not be less than 4.0. 5-121

Acceptability for Cyclic Operation

The bolts shall be acceptable for the specified cyclic application of loads and thermal stresses provided the cumulative usage factor U, as determined in 5-110.3(e), does not exceed 1.0. 5-122

GENERAL NOTES: (a) All Notes in Fig. 5-110.2.2 apply to these data. (b) Interpolation between tabular values is permissible based upon data representation by straight lines on a log-log plot. See Table 5-110.1, General Note (b).

Fatigue Strength Reduction Factor for Threads

Unless it can be shown by analysis or test that a lower value is appropriate, the fatigue strength reduction factor used in the fatigue evaluation of threaded members shall not be less than 4.0.

NOTE: (1) The number of cycles indicated shall be read as follows: I EJ p I × 10 J, e.g., 5E6 p 5 × 106 or 5,000,000.

5-130

THERMAL STRESS RATCHET IN SHELL

It should be noted that under certain combinations of steady state and cyclic loadings there is a possibility of large distortions developing as the result of ratchet action; that is, the deformation increases by a nearly equal amount for each cycle. Examples of this phenomenon are treated herein and in 5-140. (a) The limiting value of the maximum cyclic thermal stress permitted in a shell loaded by steady state internal pressure in order to prevent cyclic growth in diameter is as follows. Let y′pmaximum allowable thermal stress computed on an elastic basis, divided by the yield strength2 Sy xpmaximum general membrane stress due to pressure divided by the yield strength2 Sy Case 1. Linear variation of temperature through the shell wall:

be determined in accordance with the procedures which follow. (a) Bolts made of materials which have minimum specified tensile strengths of less than 100,000 psi (689 MPa) shall be evaluated for cyclic operation by the methods of 5-110, using the applicable design fatigue curve, Figs. 5-110.1, 5-110.2.1, 5-110.2.2, 5110.2.3, 5-110.3, and 5-110.4, and an appropriate stress concentration factor (see 5-122). (b) High strength alloy steel bolts and studs may be evaluated for cyclic operation by the methods of 5110 using the design fatigue curve of Fig. 5-120.1, provided: (1) the material is one of the following: SA-193 Grade B7 or B16, SA-320 Grade L43, SA-540 Grades B23 and B24, heat treated in accordance with Section 5 of SA-540; (2) the maximum value of the service stress at the periphery of the bolt cross section (resulting from direct tension plus bending and neglecting stress concentrations) shall not exceed 2.7Sm, if the higher of the two fatigue design curves given in Fig. 5-120.1 is used (the 2.0Sm limit for direct tension is unchanged); (3) threads shall be of a “V” type, having a minimum thread root radius no smaller than 0.003 in. (0.076 mm);

y′ p

1 for 0 < x < 0.5 x

y′ p 4(1 − x) for 0.5 < x < 1.0

Case 2. Parabolic constantly increasing or constantly decreasing variation of temperature through the shell wall: 2 It

403

is permissible to use 1.5Sm whenever it is greater than Sy.

5-130

1998 SECTION VIII — DIVISION 2

5-140

FIG. 5-110.3 DESIGN FATIGUE CURVE FOR WROUGHT 70 COPPER–30 NICKEL FOR TEMPERATURES NOT EXCEEDING 700°F

y′ p 5.2(1 − x) for 0.615 < x < 1.0

5-140

and approximately for x < 0.615 as follows: For x p y′ p

0.3 4.65

0.4 3.55

PROGRESSIVE DISTORTION OF NONINTEGRAL CONNECTIONS

Screwed-on caps, screwed-in plugs, shear ring closures, and breech lock closures are examples of non-integral connections which are subject to failure by bell-mouthing or other types of progressive deformation. If any combination of applied loads produces yielding, such joints are subject to ratcheting because the mating members may become loose at the end of each complete operating cycle and start the next cycle in a new relationship with each other, with or without manual manipulation. Additional distortion may occur in each cycle so that interlocking parts, such as threads, can eventually lose engagement. Therefore primary plus secondary stress intensities (4-134) which result in slippage between the parts of a nonintegral connection in which disengagement could occur as a result of progressive distortion shall be limited to the allowable stress limits given in 4-131 and 4-132.

0.5 2.70

(b) Use of the yield strength Sy in the above relations instead of the proportional limit allows a small amount of growth during each cycle until strain hardening raises the proportional limit to Sy. If the yield strength of the material is higher than is the endurance limit3 for the material, the latter value shall be used, if there are to be a large number of cycles, because strain softening may occur. 3 The

endurance limit shall be taken as two times the Sa value at 106 cycles in the applicable fatigue curve of Fig. 5-110.1 or two times the Sa value at 1011 cycles in the applicable fatigue curve of Fig. 5-110.2.2.

404

405 FIG. 5-110.4 DESIGN FATIGUE CURVE FOR NICKEL–CHROMIUM–MOLYBDENUM–IRON, ALLOYS X, G, C-4, AND C-276 FOR TEMPERATURES NOT EXCEEDING 800°F

NOTES: (1) E p 28.3 × 106 psi (2) Table 5-110.1 contains tabulated values and a formula for accurate interpolation of this curve.

APPENDIX 5 — MANDATORY Fig. 5-110.4

FIG. 5-120.1 DESIGN FATIGUE CURVE FOR HIGH STRENGTH STEEL BOLTING FOR TEMPERATURES NOT EXCEEDING 700°F

Fig. 5-120.1 1998 SECTION VIII — DIVISION 2

406