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AD 2000-Merkblatt ICS 23.020.30 February 2005 edition
Special cases Simplified analysis for cyclic loading
AD 2000-Merkblatt
S 1
The AD 2000-Merkblätter are prepared by the seven associations listed below who together form the “Arbeitsgemeinschaft Druck-behälter” (AD). The structure and the application of the AD 2000 Code and the procedural guidelines are covered by AD 2000-Merk- blatt G 1.
The AD 2000-Merkblätter contain safety requirements to be met under normal operating conditions. If above-normal loadings are to beexpected during the operation of the pressure vessel, this shall be taken into account by meeting special requirements.
If there are any divergences from the requirements of this AD 2000-Merkblatt, it shall be possible to prove that the standard of safety ofthis Code has been maintained by other means, e.g. by materials testing, tests, stress analysis, operating experience.
Fachverband Dampfkessel-, Behälter- und Rohrleitungsbau e.V. (FDBR), Düsseldorf Hauptverband der gewerblichen Berufsgenossenschaften e.V., Sankt Augustin Verband der Chemischen Industrie e.V. (VCI), Frankfurt/Main Verband Deutscher Maschinen- und Anlagenbau e.V. (VDMA), Fachgemeinschaft Verfahrenstechnische Maschinen undApparate, Frankfurt/Main Stahlinstitut VDEh, DüsseldorfVGB PowerTech e.V., Essen Verband der Technischen Überwachungs-Vereine e.V. (VdTÜV), Berlin
The above associations continuously update the AD 2000-Merkblätter in line with technical progress. Please address any proposals forthis to the publisher:
Verband der Technischen Überwachungs-Vereine e.V., Friedrichstraße 136, 10117 Berlin
Contents
0 Foreword
1 Scope
2 General
3 Symbols and units
4 Determination of allowable number of
load cycles
5 Design
6 Manufacture
7 Testing
8 Consideration of special operating conditions
9 Measures to be taken when the design lifetime
has been reached
10 Additional details
Annex 1: Explanatory notes on AD 2000-Merkblatt S 1
Annex 2: Example of calculation
Annex 3: Simplified analysis for cyclic loading for spher-
oidal graphite cast iron
0 Foreword
The AD 2000 Code can be applied to satisfy the basic
safety requirements of the Pressure Equipment Directive,
principally for the conformity assessment in accordance
with Modules “G” and “B + F”.
The AD 2000 Code is structured along the lines of a self-
contained concept. If other technical rules are used in
accordance with the state of the art to solve related prob-
lems, it is assumed that the overall concept has been
taken into account.
The AD 2000 Code can be used as appropriate for other
modules of the Pressure Equipment Directive or for dif
ferent sectors of the law. Responsibility for testing is as
specified in the provisions of the relevant sector of the
law.
1 Scope
1.1 The following rules on simplified analysis for cyclic
loading1) apply to pressure-bearing parts of pressure ves-
sels made of
– ferritic and austenitic rolled and forged steels,
– spheroidal graphite cast iron grades as specified in
Annex 3
manufactured and tested according to the W and HP
series of the AD 2000-Merkblätter.
1.2 The calculation only applies for components dimen-
sioned on the basis of non-time-dependent design strength
values (see 6.2 and 6.3 of AD 2000-Merkblatt B 0) and sub-
jected to cyclic loads only in the form of pressure fluctuations.
Additional cyclic loadings, for example loads due to rapid
1) The term "cyclic loading" is meant here in a comprehensive sense as the variation
over time of a loading regardless of the magnitude and arithmetic sign of the mean
value.
Supersedes October 2004 edition; | = Amendments to previous edition
AD 2000-Merkblätter are protected by Copyright. The rights of use, particularly of any translation, reproduction, extract of figures, transmission by
photomechanical means and storage in data retrieval Systems, even of extracts, are reserved to the author. Carl Heymanns Verlag has taken all reason-
able measures to ensure the accuracy of this translation but regrets that no responsibility can be accepted for any error, omission or inaccuracy. In
cases of doubt or dispute, the latest edition of the German text only is valid. ww
AD 2000-Merkblatt AD-2000-Merkblatt S 1, 02. 2005 edition Page 5
5.3 The life expectancy can be increased within the fra-mework of design evaluation according to Table 3 by, for
example, the following design measures:
(1) Hemispherical or torispherical head instead of semi-ellipsoidal head;
(2) Conical shell with knuckle instead of cone with corner
joint;
(3) Avoidance of inclined nozzles and pad reinforce-
ments;
(4) Tapered transition between tubesheets, flanges etc.and the vessel shell;
(5) Avoidance of rectangular openings.
Over-dimensioning for predominantly static loading also
leads to a greater number of allowable load cycles. Simi-larly a greater number of load cycles can normally be
permitted by applying AD 2000-Merkblatt S 2 (see An-nex 2 of this AD 2000-Merkblatt).
6 Manufacture
For the manufacture of pressure vessels the HP series ofthe AD 2000-Merkblätter applies. For vessels calculated
according to this AD 2000-Merkblatt the following re-quirements shall additionally be met:
6.1 In the case of cyclic loading, defects arising duringproduction have a more unfavourable effect than with
static loading. The component lifetime can be considera-bly reduced by notches or unfavourable residual stresses.
6.2 For the components special requirements shall beimposed on the form of welds. The requirements shall be
imposed on the form of welds. The requirements of quality level B as specified in EN 25817 shall be met. With regardto heat control during welding and welding sequence,
special attention shall be paid to the welding residualstresses. All heat treatments shall be properly performed
to meet the material and wall thickness requirements.
Annealing temperatures, holding time and cooling condi-
tions shall be fixed as far as possible such that consider-able elongation and notched bar impact toughness are
ensured. In many cases the yield point and tensilestrength will set in at the lower limit of the allowable range.
Stress relief shall be performed such that the residual stresses are reduced to a low level and the above material properties are maintained (see the corresponding stan-
dards and material data sheets).
Stamping shall not be performed at locations subject to
high loading.
7 Testing
For the testing and inspection prior to, during and aftermanufacture, the following sections shall be observed in
addition to AD 2000-Merkblätter of the HP series :
7.1 Design examination
Within the context of the design examination as described
in AD 2000-Merkblatt HP 511, the relevant third party shallestablish the locations which shall be tested in particularwith regard to cyclic loading in the tests described in 7.2
and 7.3.
7.2 Tests during production and final test
7.2.1 The tests to be performed during production by themanufacturer or within the final test by the relevant third
party shall ensure that there are no defects present in thepressure vessel or pressure vessel component which may
grow rapidly in size under cyclic loading and which may result in failure of the pressure parts before the allowablenumber of load cycles has been reached (see AD 2000-
Merkblatt HP 5/1).
7.2.2 For the non-destructive test, the provisions of AD
2000-Merkblatt HP 5/3 in conjunction with the generaltable for HP 0 shall be observed. If according to this, the
method of non-destructive examination is left open, theultrasonic examination should be given preference. Loca-
tions subject to high loadings during operation such as welded-in nozzles, hole edges or cross sectional transi-
tions, shall as far as practicable be subjected completely to non-destructive testing. The visual examination forsurface defects and external visible welding defects shall
be performed with appropriate care.
7.3 Inspections during operation
7.3.1 Each pressure vessel for which the number ofallowable load cycles (cycle number N) has been fixed
shall undergo an internal inspection at the latest when half
of the load cycles fixed has been reached.
As a result of the type of operation, the intervals betweeninternal tests may be shorter in accordance with national
regulations.
The user is obliged to record the number of load cycles
arising by suitable means and, if necessary, to arrange forthe internal inspections.
7.3.2 If the operating conditions assumed in the calcula-tion under clause 4 deviate in terms of a greater cyclic
loading or if damage to the pressure-bearing wall is to beexpected before the end of the inspection intervals owing
to other operational influences, they shall be reduced inaccordance with national regulations.
Longer inspection intervals will possibly result from calcu-
lations according to AD 2000-Merkblatt S 2.
7.3.3 In the case of pressure vessels subject to cyclic
loading, in-service inspections are of particular impor-tance; they-permit early detection of incipient damage.
For this purpose, the internal inspections shall be supple-mented by non-destructive tests on highly loaded loca-
tions. Surface crack tests and ultrasonic tests are themethods to be considered here. For the examination of
readly accessible areas, the outside surface of the vessel can also be subjected to ultrasonic testing.
7.3.4 If no cracks are detected during an internal inspec-
tion, the next internal inspection shall be performed fol-lowing special agreement, and be within the shortest
interval specified in applicable national regulations. How-ever, the inspection shall be performed no later than when
half the number of load cycles has been reached. Thisalso applies if the allowable number of load cycles is ex-
ceeded.
7.3.5 The inspections described in 7.3.1 to 7.3.4 for
cyclic loading during operation may be waived if the com-ponent is designed to withstand an operational load cycle
number of 2 ⋅ 106.
7.3.6 At low permissible temperatures below –200 °C,
the intervals for carrying out internal inspections shall again be halved, i.e. internal inspections carried out in
accordance with 7.3.1 and 7.3.4 shall be carried out whena quarter of the specified number of stress cycles have
AD 2000-Merkblatt Page 6 AD-2000-Merkblatt S 1, 02. 2005 edition
8 Consideration of special operating conditions
In the case of corrosion-induced crack formation (fatigue
crack corrosion, strain-induced crack corrosion), hydro-gen-induced crack formation in compressed hydrogen, or
the presence of a magnetite protective layer, the provi-sions of AD 2000-Merkblatt S 2, shall be applied accord-
ingly.
In cases of doubt a calculation according to AD 2000-
Merkblatt S 2 shall be conducted.
9 Measures to be taken when the design lifetime has been reached
9.1 If the allowable number of load cycles for a compo-nent or the allowable value for cumulative damage ac-
cording to clause 4 has been reached, non-destructivetests according to 7.3 shall be performed as completely
as possible at a certain number of highly loaded locationsto be laid down with the relevant third party.
9.2 If no cracks are found in the tests conducted as
described in 9.1, continued operation is permitted. Theprerequisite for this is that no fatigue damage is found in
the non-destructive tests conducted in the inspectionintervals which correspond to 50 % of the operating time
specified in 9.1. After this operating time has beenreached, further measures shall be agreed for each indi-
vidual case in accordance with national regulations.
At low permissible temperatures below –200 °C, the inter-
vals for carrying out non-destructive tests shall be re-duced from 50 % to 25 % of the operating time in accor-dance with 9.1.
9.3 Should cracks or crack-type defects within themeaning of 5.2 and 5.4 of AD 2000-Merkblatt HP 5/3 or
other more extensive damage established in the tests carried out as described in 9.1 or 9.2, the component or
the structural element concerned shall be replaced, unless continued operation is deemed to be permitted by virtue
of appropriate measures to be agreed in accordance withnational regulations.
9.4 The following design, manufacturing and process-related measures can be considered to allow continuedoperation:
(1) Removal of cracks by grinding. If as a result of grind-ing too thin a wall thickness is obtained repair welding
shall only be carried out in cooperation with themanufacturer within the context of the national regula-tions;
(2) Grinding the welds to remove all notches;
(3) Removal of restraints to expansion: e.g. replacement
of cracked rigid stiffeners by joints not restraining ex-pansion;
(4) Change in mode of operation.
10 Additional details
10.1 In all cases where the conditions for waiving appli-cation of this Merkblatt as described in 1.4 an 1.5 are notmet, this shall be indicated to the manufacturer and for
the design examination of the relevant third party. In suchcases, measures adapted to operational needs shall be
provided for and, if necessary, agreed between the manu-facturer, customer/user and relevant third party. These
measures shall be included in the design-approved draw-ing and in the certificate of the final test, making reference
to AD 2000-Merkblatt S 1.
10.2 The following items shall be indicated in conformity
with the scope given in clause 1 (internal pressure fluctua-tions only):
– Number of pressure fluctuations between unpressur-
ised state and maximum allowable pressure (start-upsand shutdowns);
– Pressure fluctuations of constant amplitude which aresuperimposed on the working pressure, and their num-
ber of operational load cycles;
– Pressure fluctuations of various load cycle groups and
their number of operational load cycles for a specified operational load regime;
– Minimum and maximum temperature during a load cycle or, in the case of load regime, in the individual load cycle groups.
AD 2000-Merkblatt Page 18 AD-2000-Merkblatt S 1, 02. 2005 edition
Table 3. Examples of structural forms and welded joints with the corresponding classes (K 0, K 1, K 2 and K 3) andcorresponding stress factors η (cracks drawn in as examples)
SerialNo. Illustration Description Requirements Class η
7.5
Reinforcing plate, backing plate connected with fillet weld. Noapplication of alternating addi-tional forces and moments
s2 ≤ 1,5 ⋅ s1
r ≥ 2 ⋅ s2
K 2 2,0
7.6 full-penetration welded from bothsides
K 1
7.7
welded attachments with applica-tion of additional forces andmoments
Welded from both sides, but not fully penetrating
K 2
3,0
8. Welded attachments without application of alternating additional forces or moments. Examples
Prerequisite: external findings of attachment welds to EN 25817, quality level B, excluding weld reinforcement and weld sag andunequal leg fillet weld
8.1
vessel-to-skirt supportconnection
welded from one side K 2 2,0
8.2 vessel wall with support ring K 2
8.3
welded from both side, but not fully penetrating
K 2
8.4
vessel all with stiffening ring
welded with interruption incircumferential direction
K 3
8.5
vessel wall with supporting lug(with or without backing plate)
welded from one side K 2
8.6
vessel wall with support foot(with or without backing plate)
AD 2000-Merkblatt AD-2000-Merkblatt S 1, 10. 2004 edition Page 19
Table 3. Examples of structural forms and welded joints with the corresponding classes (K 0, K 1, K 2 and K 3) andcorresponding stress factors η (cracks drawn in as examples)
SerialNo.
Illustration Description Requirements Class η
8.7 vessel wall with trunnion (with or without backing plate)
welded from one side K 2 2,0
8.8 vessel wall with lifting lug(with or without backing plate)
welded from one side K 2
8.9 vessel wall with bracket welded from one side K 2
AD 2000-Merkblatt AD-2000-Merkblatt S 1, 02. 2005 edition Page 21
1z15==
e·p
SK – z1 z acc. to Figs. 3.1 to 3.7 in
AD 2000-Merkblatt B 2
according to 8.1.2
psDSK ·+
cos== K–
20 · s
according to Annex to AD 2000-Merkblatt B 2
2zvg e·
10p== σσ z2 z acc. to Table A 1
+⋅
⋅==∧
11
sco
2
K
2
sD
emax
z
ϕσση
For parameter calculations for this, see Fig. A 4.
Excluding the shallow conical shells (ϕ = 60–70°), which
are hardly used in practice, for pressure vessels under
cyclic pressure loading, a stress factor of η = 2,7 was
fixed accordingly in Table 3, No. 1.10/1.11.
Explanatory note on 4.1.3, Formula (3)
In order to take into account the cyclic-strength-reducing
influence of the component size, the correction factor Fd
was taken for welded joints in the endurance range given
in 7.2.6 of AD 2000-Merkblatt S 2. Dependence on thenumber of load cycles according to AD 2000-Merkblatt
S 2, formula (17), was dispensed with.
The Fd factor is also used by way of simplification for
unwelded components.
Explanatory notes on 4.2 and Figure 6
To plot a load cycle curve for unwelded components (sur-
face condition: rolling skin), calculations were conducted according to AD 2000-Merkblatt S 2 for different materials taking account of the influence of plasticity and maximum
mean stress (σ = Rp 0,2).
According to Fig. A 1 of this Annex, it is possible to indi-cate by approximation a “mean value” curve with constant
gradient exponent m = 3,5 on a double-logarithmic scale. This load cycle curve class K 0 is almost identical with the
load cycle curves for unwelded component areas accord-ing to the British Standard BS 5500 : 94 [4] or, as the casemay be, BS 7608 : 1993 [5] (curves of class C).
For welded joints, the load cycle curves of classes K 1,K 2 and K 3 from AD 2000-Merkblatt S 2 were taken.
To check the influence of plasticity in the range of lownumbers of load cycles, calculations were conducted
(conservatively) according to AD 2000-Merkblatt S 2 forthe low-strength material H II. Fig. A 4 shows that the
reduction through the ke factors (ke > 1) is relatively small
from 1000 load cycles on and only takes effect in classes
K 1 and K 2. In view of the scoope (N ≥ 1000), a global
stress increase in elastic-plastic range through ke factors
was therefore dispensed with for reasons of simplification.
For reasons of practicability (easier readability for fasterdetermination of allowable load cycles), the semi-
logarithmic presentation was chosen for the cyclic load chart as in the previous AD-Merkblatt S 1 (Edition 3.90),
Fig. 2 (N100 curves).
Explanatory note on 4.3 and Figure 7
In compliance with the former representation of the N100
and fL curves, similar curves for pressure vessels of cer-
tain design and operational boundary conditions were taken over.
Formula (8) is obtained from Formula (6) with B = 7940
from Table 1 for class K 1 and η = 3,0.
Explanatory note on 4.4
To simplify the procedure with damage accumulation in
the case of an operational load regime, no fictitious loadcycle curves according to the Haibach modification as inAD 2000-Merkblatt S 2 are contained in the endurance
range (N > 2 · 106).
As compared with the base values of allowable stress
amplitudes 2σa according to AD 2000-Merkblatt S 2, Ta-
ble 4 in the range N = 2 · 106 to 108 and in accordance
with the procedure according to AD 2000-Merkblatt S 2,
9.2, stress amplitudes with N ≥ 2 · 106 at a level of 50 %
of the endurance values 2σaD according to Table 2 of this
AD 2000-Merkblatt are regarded as negligible.
Literature
[1] AD 2000-Merkblatt S 2: Analysis for cyclic loading,
October 2004 editionHeymanns Verlag, Cologne
[2] AD 2000-Merkblätter, Series B.Heymanns Verlag, Cologne
[3] Richtlinienkatalog Festigkeitsberechnungen (RKF),Behälter und Apparate Part 5.
Edition 1986. Linde-KCA-Dresden GmbH
[4] British Standard BS 5500/1994: Specification forunfired fusion welded pressure vessels
[5] British Standard BS 7608/1993: Code of practice for fatigue design and assessment of steel structures
[6] Duan-Shou Xie and Yong-Gou Lu: Prediction of
Stress Concentration Factors for Cylindrical PressureVessels with Nozzles.
Int. J. Pressure Vessel & Piping 21 (1985)
[7] Gorsitzke, B.: Vorhersage der Ermüdungsfestigkeit
druckführender Komponenten im Energie- und Che-mieanlagenbau, Part 1 and Part 2
Z. TÜ 30 (1989) No. 2 and No. 3
[8] Gorsitzke, B: Neuere Berechnungsvorschriften zur
Ermüdungsfestigkeit von Druckbehältern.
Z. TÜ 36 (1995) No. 6 and Nos. 7/8
[9] Gorsitzke, B.: Erläuterungen zum neuen AD-Merkblatt
S 1 „Vereinfachte Berechnung auf Wechselbean-spruchung und ergänzende Hinweise“.
Fig. A 2. Allowable number of load cycles as a function of stress range according to AD 2000-S 2 for welded joints at ambitaking into account the influence of plasticity (k factors)
AD 2000-Merkblatt AD-2000-Merkblatt S 1, 02. 2005 edition Page 29
Annex 3 to AD 2000-Merkblatt S 1
Simplified analysis for cyclic loading for
spheroidal graphite cast iron
1 Scope and general
1.1 The following rules on simplified analysis for cyclic
loading apply to pressure-bearing unwelded parts ofpressure vessels made of spheroidal graphite cast iron
according to DIN EN 1563, limited to the grades EN-GJS-400-15/15U, EN-GJS-400-18/U-LT and EN-GJS-350-
22/22U-L, manufactured and tested according to AD2000-Merkblatt W 3/2.
1.2 The external and internal conditions of the castings shall meet stricter requirements that reflect the require-ments of quality leves A and B as specified in DIN 1690
Part 10 (see 4.2).
1.3 If the number of load cycles with pressure fluctua-
tions between the unpressurized condition and the maxi-mum allowable pressure p (start-ups and shutdowns) and
the range (p–p) of any number of pressure fluctuations
relative to p1) do not exceed the following values, this
annex need not be used.
a) N100 ≤ 100000 and (p–p) ≤ 50 % of p1) for EN-GJS-400-
15/15U
b) N100 ≤ 6000 and (p–p) ≤ 35 % of p1) for EN-GJS-400-
18/18U-LT and EN-GJS-350-22/22U-LT
Here, geometries with a shape-dependent stress factor ηnot exceeding 3,5 are assumed.
The limit values of the number of load cycles N100 may be
increased to 2,4 times if the test conditions correspondingto quality level A are met.
1.4 Unless otherwise specified in this annex, all the otherrules in the main body of this AD 2000-Merkblatt are
applicable.
2 Determination of allowable number of
load cycles
2.1 The fictitious pseudoelastic stress range for de-termining the allowable number of load cycles shall be
calculated according to formula (2). In this, the stress
factor η shall be estimated from Table 3. Here, values
greater than η = 2,5 need not be taken into accoount. For
structures that cannot be classified according to this ta-
ble, the η values shall be proven unless η = 2,5 has been
included in the calculation.
The wall thickness correction factor Fd shall be calculated
as appropriate according to formula (3) and instad of theexponent 0,25 the value 0,1 shall be used and for wall
thicknesses se > 150 mm the correction factor shall be
limited to Fd = 0,84. Formula (4) applies for the tempera-
ture correction factor fT*.
2.2 The allowable number of load cycles for component
areas with cast skin surfaces in the range 10³ ≤ N ≤ 2 · 106
shall be calculated as a function of the stress range ac-cording to formula (2), if necessary from formula (6) with
m = 8,333.
1) The calculation pressure pr may also be used instead of p.
The calculation constant B values shall be taken from
Table A 1. Here, the notch effects from surface roughnessand the maximum possible influence of working pressure
mean stresses have already been taken into account.
The knee-point number of load cycles ND from which the
fatigue behaviour is no longer dependent on the number
of load cycles is fixed at N = 2 · 106. For quality level A,
the allowable number of load cycles may also be takenfrom Figure A 6.
The design curves shown in Figure A 6 are based ondamage curves corresponding to a failure probabilitiy ofapproximately 2,3 % (see [1]).
Table A 1. Calculation constants B and strength
characteristic values 2 σaD
Constant B103 ≤ N ≤ 2 · 106
2σaD [N/mm2]
N ≥ 2 · 106
Quality level A B A B
Material grade
EN-GJS-
400-15/15U EN-GJS-
400-18/18U-LT
787 708 138 124
EN-GJS-
350-22/22U-LT
732 659 128 116
2.3 For the spezial case of pressure-bearing parts with
geometries with a shape-dependent stress factor η= 2,5,
temperatures T* ≤ 100 °C, wall thicknesses se ≤ 25 mm
and pressure fluctuations between 0 and pr, the allowable
number of load cycles in the range 1000 ≤ Nzul ≤ 2 · 106
may be determined according to
Nzul = N100 · fL (A1)
with
N100 = [B / (2.5 · K20/S)]8.333 (A2)
fL = [pr / (p–p)]8.333 (A3)
The values N100 and fL may also be taken from Figure A 7
and Figure A 8.
The acceptable pressure fluctuation range relative to pr for
these vessels for a number of load cycles N ≥ 2 · 106 shall
be calculated according to
(p–p) / pr = 2σaD / 2,5 · K20/S) (A4)
with 2σaD from Table A 1.
2.4 The calculation procedure to take into account anoperational load regime shall be carried out as appropriate
according to 4.4 of the main body of this AD 2000-Merkblatt. The damage portions of load regimes whose
stress range 2σaD is less than 70 % of the 2σaD values may
be disregarded here.
3 Design
3.1 When designing castings, it shall be noted that de-
signs may be produced that are covered with a stress
factor η = 2,5. If it is not possible to estimate the η value
(see stress factors η in Table 3), detailed proof of the
stress factor η or a calculation according to annex 5 of AD