Engineering task and calculation objective
The AN3F module determines the maximum permissible number of load cycles under fatigue loading to ASME BPVC Section VIII, Division 2, Annex 3-F in conjunction with Part 5. From the stress range of a load cycle, the alternating stress intensity is formed and converted via the material-dependent design fatigue curve into the allowable number of cycles — the basis of every fatigue assessment using the smooth-bar method of Division 2.
Annex 3-F provides the fatigue curves for the material groups — among others for carbon and low alloy steels (depending on tensile strength), high alloy austenitic steels, and nickel alloys. The module selects the governing curve according to material and stress level, corrects the stress amplitude with the ratio of the moduli of elasticity, and interpolates intermediate values with exact logarithmic interpolation, so that no conservative step jumps occur between the tabulated points.
This calculation is needed whenever a pressure vessel is fatigue-relevant after the screening in Part 5: under cyclic pressure operation, temperature cycling, start-up and shutdown transients, or varying external loads. The result is the allowable number of cycles N per load cycle type, from which the total fatigue usage follows via damage accumulation.
Standard and calculation basis: ASME BPVC 2017, Section VIII-Division 2, Annex 3-F; Part 5
Calculation workflow
- Determine the stress range: From the stress analysis (elastic per Part 5), the range of the principal stress differences between the two extreme states of each load cycle is determined — including stress concentrations and, where applicable, the Ke correction when the elastic limits are exceeded.
- Form the alternating stress intensity: Half the stress range yields the alternating stress intensity S_alt. It is corrected with the ratio of the modulus of elasticity of the fatigue curve to the modulus of the component at operating temperature, since the curves in Annex 3-F are referenced to a reference modulus.
- Select the governing fatigue curve: According to the material group and — for ferritic steels — the tensile strength, the applicable design curve is selected from Annex 3-F. For carbon and low alloy steels, in the low-cycle regime the applicable curve additionally depends on the stress level.
- Determine the allowable number of cycles: From S_alt, the curve yields the maximum permissible number of load cycles N. Between the tabulated points, logarithmic interpolation is used; the intermediate values reported by the module make the interpolation traceable.
- Evaluate the damage accumulation: If several cycle types occur, the ratio of actual to allowable number of cycles is formed for each and summed according to Miner's rule. The sum of the partial damages must remain less than or equal to 1.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Material | Materialangaben | – |
| S12 | Δσ1,2 = σ1-σ2 = | N/mm² |
| S23 | Δσ2,3 = σ2-σ3 = | N/mm² |
| S13 | Δσ1,3 = σ1-σ3 = | N/mm² |
| Stress intensity range | Srij | N/mm² |
| Material yield strength | σys | N/mm² |
| Ultimate tensile strength | σuts | N/mm² |
| Modulus of elasticity at operating temperature | ET | N/mm² |
| Fatigue strength reduction factor acc. table 5.11 and 5.12 | Kf | – |
| Parameter according to table 5.13 | m | – |
| Parameter according to table 5.13 | n | – |
| Snk | (PL+Pb+Q) Sn,k | N/mm² |
| Allowable stress | S | N/mm² |
| Allowable limit on the primary plus secondary stress range | SPS | N/mm² |
| Auxiliary variable | mSPS | – |
| Fatigue penalty factor | Ke,k | – |
| Alternating stress intensity | Salt | N/mm² |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Intermediate value | Y | – |
| Intermediate value | 10Y | – |
| Intermediate value | X | – |
| Maximum number of load cycles | N | – |
Calculation options
Material
Carbon, low-alloy and high-alloy steels, high-tensile steels · Series 3XX high-alloy steels · Wrought 70-30 copper-nickel steels · Nickel-Chromium-Molybdenum.Iron · High strength bolting for maximum nominal stress ≤ 2.7 S_M · High strength bolting for maximum nominal stress > 2.7 S_M
Frequently asked questions
Are the fatigue curves in Annex 3-F mean curves or design curves?
They are design curves: compared to the test mean values on polished small-scale specimens they already contain safety factors (classically a factor of 2 on stress or 20 on cycles, whichever is more conservative) covering scatter, size effect, and surface condition. Additional blanket safety margins on N should therefore not be applied — but correct stress determination including notch effects is essential.
Why must the stress amplitude be corrected with the modulus ratio?
The curves were determined on a strain basis and converted using a fixed reference modulus of elasticity. If the modulus of the component material at operating temperature deviates from it, S_alt must be scaled by E_curve/E_component, otherwise the actual strain amplitude is misjudged — a non-negligible effect at high temperatures.
When can the detailed fatigue analysis be waived?
Part 5 contains screening criteria: if the expected number of cycles from pressure, temperature, and supplemental load variations stays below the limits defined there, the vessel is considered not fatigue-critical and Annex 3-F need not be applied. The screening must be documented; if it fails, the full analysis must be performed for all relevant cycle types.
Do the curves also apply to welds?
The smooth-bar curves per Annex 3-F apply to the base material, and to welds only if their notch effect is captured in the stress analysis via fatigue strength reduction factors or stress concentration factors. Alternatively, Division 2 offers with the structural stress method (Annex 3-D context, Part 5.5.5) a dedicated procedure specifically for welded details that directly incorporates weld quality.