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APPENDIX 5 — MANDATORY
DESIGN BASED ON FATIGUE ANALYSIS
ARTICLE 5-
5-100 ANALYSIS FOR CYCLIC
OPERATION
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 AD- 160, 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- 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, 5- 110.3, and 5-110.4.^1 These curves show the allowable amplitude Sa of the alternating stress component (one- half of the alternating stress range) plotted against the
(^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 temper- atures 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.
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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 di- rectly 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 4- 137 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).
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 DESIGN FOR CYCLIC LOADING
5-110.1 Determination of Vessel’s Ability to With- stand 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
5-110.1 1998 SECTION VIII — DIVISION 2 5-110.
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.
5-110.2 Significance of Compliance With Require- ments 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. Subpara- graphs 5-110.3(a) and 5-110.3(b) apply to the determina- tion 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 s 1 , s 2 , and s 3 for later identification. (2) Stress Differences. Determine the stress differ- ences
S 12 p s 1 − s 2
S 23 p s 2 − s 3
S 31 p s 3 − s 1
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
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stress cycle, it is necessary to use the following more general procedure. (1) Consider the values of the six stress compo- nents s t , s l , s r , t lt , t lr , and t rt 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 com- ponents 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 s ti , s li , etc., from the corresponding stress components s t , s l , 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,
S ″ 12 p s′ 1 − s′ 2
S ″ 23 p s′ 2 − s′ 3
S ″ 31 p s′ 3 − s′ 1
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 3 Sm limit (see 4-134). (d) The alternating stress intensity S alt is one half the value of Srij. (e) Design Fatigue Curves. Figures 5-110.1, 5- 110.2.1, 5-110.2.2, 5-110.3, and 5-110.4 contain applica- ble 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
5-110.3 1998 SECTION VIII — DIVISION 2 5-110.
TABLE 5-110. TABULATED VALUES OFSa , ksi, FROM FIGURES INDICATED
Number of Cycles 1
Figure Curve 1E1 2E1 5E1 1E2 2E2 5E2 8.5E2^2
5-110.1 UTS 115–130 ksi 420 320 230 175 135 100... 5-110.1 UTS ≤ 80 ksi 580 410 275 205 155 105... 5-110.2.1... 708 512 345 261 201 148... 5-110.2.2... See Table 5-110. 5-110.3 Sy p 18.0 ksi 260 190 125 95 73 52... 5-110.3 Sy p 30.0 ksi 260 190 125 95 73 52... 5-110.3 Sy p 45.0 ksi 260 190 125 95 73 52 46 5-110.4... 708 512 345 261 201 148... 5-120.1 MNS^3 ≤ 2.7Sm 1150 760 450 320 225 143... 5-120.1 MNS^3 p 3 S (^) m 1150 760 450 300 205 122...
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 > S (^) j , N N (^) i
p 1 Nj
Ni 2
[log (Si /S)] / log (Si /Sj )
where S, S (^) i , S (^) j p values ofSa N, N (^) i , N (^) j 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 cyclesN forSa p 53.5 ksi when UTS ≤ 80 ksi in Fig. 5-110.1. N 2000
p 1
5000
[log (64/53.5)] / log (64/48)
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 × 10 2 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 tempera- ture value. The design fatigue curves are defined over a cyclic range of 10 to 10^6 cycles, except that for nickel– chromium–molybdenum–iron alloy, a cyclic range of 10 to 10^8 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 10^11 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. 5- 110.2.3. (f) Use of Design Fatigue Curve. Multiply S alt [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
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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 n 1 , n 2 , n 3 , etc., respectively. In determining n 1 , n 2 , n 3 , etc., consid- eration 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 varia-
5-110.3 APPENDIX 5 — MANDATORY 5-
TABLE 5-110. TABULATED VALUES OFSa , ksi, FROM FIGURES INDICATED
Number of Cycles 1
1E3 2E3 5E3 1E4 1.2E4^2 2E4 5E4 1E5 2E5 5E5 1E6 2E6 5E6 1E7 2E7 5E7 1E 78 62 49 44 43 36 29 26 24 22 20.................. 83 64 48 38... 31 23 20 16.5 13.5 12................... 119 97 76 64... 55.5 46.3 40.8 35.9 31.0 28...................
44 36 28.5 24.5... 21 17 15 13.5 12.5 12................... 44 36 28.5 24.5... 19.5 15 13 11.5 9.5 9................... 39 24.5 15.5 12... 9.6 7.7 6.7 6.0 5.2 5................... 119 97 76 64... 56 46.3 40.8 35.9 26.0 20.7 18.7 17.0 16.2 15.7 15.3 15. 100 71 45 34... 27 22 19 17 15 13................... 81 55 33 22.5... 15 10.5 8.4 7.1 6 5...................
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:
n 1 p 1000
S alt 1 p (60,000 + 50,000) /2 p 55,000 psi
Type 2 cycle:
n 2 p 9000
S alt 2 p (50,000 + 0) /2 p 25,000 psi
(2) For each type of stress cycle, determine the alternating stress intensity S alt by the procedures of (a) or (b) above. Call these quantities S alt 1 , S alt 2 , S alt 3 , etc. (3) For each value S alt 1 , S alt 2 , S alt 3 , etc., use the applicable design fatigue curve to determine the maximum number of repetitions which would be allow- able if this type of cycle were the only one acting. Call these values N 1 , N 2 , N 3 , etc. (4) For each type of stress cycle, calculate the usage factors U 1 , U 2 , U 3 , etc., from
U 1 p n 1 / N 1
U 2 p n 2 / N 2
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U 3 p n 3 / N 3
etc. (5) Calculate the cumulative usage factor U from
U p U 1 + U 2 + U 3 +...
etc. (6) The cumulative usage factor U shall not ex- ceed 1.0.
5-111 Local Structural Discontinuities These effects shall be evaluated for all conditions using stress concentration factors determined from theo- retical, experimental, or photoelastic studies or finite element stress analysis techniques. Experimentally deter- mined 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.
5-112 Fillet Welds Fillet welds shall not be used in vessels for joints of Categories A, B, C, or D (see Fig. AD-400.1),
APPENDIX 5 — MANDATORY Fig. 5-110.2.
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 ANDSa ≤ 28.2 ksi (USE FIG. 5-110.2.1 FORSa > 28.2 ksi)
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5-112 1998 SECTION VIII — DIVISION 2 5-
FIG. 5-110.2.3 GRAPHICAL PRESENTATION OF CRITERIA FOR USE OF CURVES IN FIG. 5-110.2.
except as permitted for joints of Category C for slip- on 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
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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
5-130 1998 SECTION VIII — DIVISION 2 5-
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.
and approximately for x < 0.615 as follows:
For x p 0.3 0.4 0. y ′ p 4.65 3.55 2.
(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 limit^3 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 S (^) a value at 106 cycles in the applicable fatigue curve of Fig. 5-110.1 or two times the S (^) a value at 10 11 cycles in the applicable fatigue curve of Fig. 5-110.2.2.
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5-140 PROGRESSIVE DISTORTION OF
NONINTEGRAL CONNECTIONS
Screwed-on caps, screwed-in plugs, shear ring closures, and breech lock closures are examples of non-integral con- nections 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 pri- mary 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.
APPENDIX 5 — MANDATORY Fig. 5-110.
NOTES:
(1) E
p
28.3 × 10
6 psi
(2) Table 5-110.1 contains tabulated values and a formula
for accurate interpolation of this curve.
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
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