Engineering task and calculation objective
The S1 module performs the simplified fatigue analysis for pressure vessels to AD 2000-Merkblatt S1 of the German AD 2000 pressure vessel code. If a vessel is operated under fluctuating loads – i.e. with recurring pressure and temperature cycles – material fatigue can lead to crack initiation long before the static load-carrying capacity is reached. Steels with high yield strength are particularly affected, because the static design permits high stress ranges there. The verification ensures that the number of pressure fluctuations expected in operation does not exceed the allowable number of load cycles.
The simplified method works without a detailed stress analysis: from the notional pressure, the pressure fluctuation range, the wall thickness and the nominal design strength, a fictitious pseudo-elastic equivalent stress range is formed. Via correction factors for wall thickness influence and temperature influence, and via the weld class (welded/non-welded, weld quality), the allowable number of load cycles then follows from the S-N (Woehler) curve of the code.
In practice, the verification to AD 2000 S1 is needed, for example, for air receivers, autoclaves, separators downstream of reciprocating compressors or batch-operated reactors – wherever calculating and documenting load cycles is part of the design or of a periodic inspection.
Standard and calculation basis: AD 2000 S1: 2019-05
Calculation workflow
- Define the loading cycle: The inputs are the notional pressure (referred to the loading determined according to the calculation standard, e.g. AD 2000), the pressure fluctuation range, and the maximum and minimum cycle temperatures, from which the determining design temperature follows.
- Classify component and material: The nominal design strength and safety factor of the material, the wall thickness, the material group (austenite or ferrite) and the weld class of the governing detail are established. The class distinguishes non-welded regions and welds of different workmanship quality.
- Form the stress range: From the pressure fluctuation range, the wall thickness and the stress factor, the fictitious pseudo-elastic equivalent stress range is calculated – a notional quantity that also represents overelastic loading in linear-elastic terms.
- Apply the influence factors: The correction factor for wall thickness influence and the temperature influence factor reduce the endurable stress range: thicker walls and higher cycle temperatures shorten the fatigue life. Different temperature functions apply for austenite and ferrite.
- Read off the allowable number of load cycles: Using the design constant of the governing S-N curve, the allowable number of load cycles is determined and checked against the fictitious fatigue limit for N ≥ 2·10⁶. If the stress range is below that limit, the number of load cycles is computationally unlimited; otherwise the number of operating cycles must stay below the result.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Nominal design strength | K20 | N/mm² |
| Safety factor | S | – |
| Weld class | K (0 - 3) | – |
| Material ( austenite = 1 ferrite = 2) | WKST | – |
| Wall thickness | se | mm |
| Vessel pressure | Pr | bar |
| Pressure fluctuation range | (Pmax-Pmin) | bar |
| Maximum cycle temperature | Tmax | °C |
| Minimum cycle temperature | Tmin | °C |
| Determining design temperature | T* | °C |
| Correction factor for wall thickness | Fd | – |
| Temperature influence factor | fT* | – |
| Stress factor | η | – |
| Design constant | B | N/mm² |
| Fictitious pseudo-elastic stress range | 2σa* | N/mm² |
| Fictitious fatigue limit for N ≥ 2·106 | 2σaD | N/mm² |
| Allowable number of load cycles | Nzul | – |
| (according to calculation standard, e. g. AD2000) | Vorschrift | – |
Frequently asked questions
When is the simplified verification to S1 sufficient, and when is a calculation to S2 required?
S1 works with blanket, conservative assumptions: the stress range is estimated from the pressure cycle via factors, without knowing the actual stress distribution. If the allowable number of load cycles determined this way is sufficient for the operation, the verification is complete. If it is exceeded, or if complex loadings are present (temperature transients, external loads, notch details), the detailed verification to AD 2000 S2 with real stress ranges must be carried out – it usually yields higher allowable cycle counts.
What does the weld class mean for the result?
The class describes the notch severity of the governing detail. Non-welded parent material endures the highest stress ranges; welds are grouped, depending on their execution (ground flush, as-welded, welded from one side), into classes with markedly lower S-N curves. A difference of one class can change the allowable number of load cycles severalfold – weld dressing is therefore an effective means of extending fatigue life.
Why do wall thickness and temperature act as reductions?
With increasing wall thickness, the fatigue strength decreases (size effect: higher probability of defects, less favourable stress gradient); the correction factor for wall thickness influence captures this above the reference thickness. The temperature influence factor accounts for the strength decreasing with temperature, with ferrite and austenite treated differently. Both factors reduce the endurable stress range compared with the room-temperature reference value.
Does every pressure cycle count equally, including partial cycles?
No. What matters is the pressure fluctuation range of the respective cycle. Partial cycles with a smaller fluctuation range produce smaller stress ranges and consume correspondingly less fatigue life. If cycles of different magnitude occur, they must be combined via a damage accumulation; in the simplified method, the calculation is frequently carried out conservatively with the largest cycle applied to all load cycles.