1. Fatigue analyses

Two options for fatigue analyses are available

  • Stress time series and an S-N curve

  • Tension time series and a T-N curve

1.1. Analysis procedure

In both cases the fatigue analysis is carried out in the following steps:

  • Retrieve the response time series from the preceding simulation:

    • Tension and bending moment time series for S-N fatigue calculations

    • Tension time series for T-N fatigue calculations

  • Extract the time interval if specified by the user. This may be used to exclude transient response at the beginning of the simulation from the fatigue calculations.

  • For S-N fatigue analysis only:

    • calculate stresses from tension and bending moment, multiplying with any specified stress concentration factor (SCF)

  • Identify cycles in the time series using the Rainflow counting algorithm and put into bins with different ranges

  • Calculate the number of cycles to failure for each bin using the S-N or T-N curve

  • Calculate the damage from the cycles in each bin as the number of cycles in the bin divided by the number of cycles to failure for this bin. The total damage is found as the sum of the damages in the individual bins using the Miner-Palmgren equation. This is the damage from the cycles found in (the specified interval of) the time series.

  • The fatigue damage per year in the conditions in the simulations is found using the zero-crossing period of the stress or tension timeseries.

1.2. S-N curve input and stress calculation

Stresses are calculated from the tension and bending moments using the Cross Sectional Area, Section Modulus and stress concentration factor SCF:

\(\mathrm {\sigma _{ab} = SCF \times ( \frac{F}{A} - sin(\alpha) \times \frac{M_y}{W} - cos(\alpha) \times \frac{M_z}{W} ) }\)

Where:

  • \(\mathrm {\sigma _{ab}}\): Stress in axial direction from tension and bending moments

  • \(\mathrm {SCF}\): Stress Concentration Factor

  • \(\mathrm {F}\): Tension

  • \(\mathrm {A}\): Cross Sectional Area for calculation of stress from tension

  • \(\mathrm {\alpha}\): Angle clockwise from local element y-axis to point on circumference for stress calculation. See Sign convention for internal loads for the bending moment sign convention.

  • \(\mathrm {M_y}\): Bending moment about the local element y-axis

  • \(\mathrm {M_z}\): Bending moment about the local element z-axis

  • \(\mathrm {W}\): Section Modulus for calculation of stress from bending moment

The default values for Cross Sectional Area and Section Modulus are taken from the cross-section specification.

If no S-N curves are available in the drop-down menu, right-click on Model, then select New → SN Curve. A number of predefined S-N curves are available or a new S-N curve may be defined.

A thickness correction will be included in the fatigue calculations if

  • the S-N curve is specified with nonzero values for Reference Thickness and Thickness Correction Exponent

  • a nonzero Effective Thickness is specified in the fatigue analysis input

1.3. T-N curve input

The T-N curve is defined as

\(\mathrm {N \times (\frac{\Delta S}{RBS})^m = k}\)

or

\(\mathrm {N = \frac{k} {(\frac{\Delta S}{RBS})^m}}\)

giving a straight line in log scale for log cycles as a function of log tension range:

\(\mathrm {logN=log(k) + m \times log(RBS) - m \times log(\Delta S)}\)

Where:

  • \(\mathrm {N}\): Number of cycles to failure

  • \(\mathrm {\Delta S}\): Tension range

  • \(\mathrm {m}\): Slope in T-N curve

  • \(\mathrm {k}\): Constant in T-N curve

  • \(\mathrm {RBS}\): Reference Breaking Strength

  • \(\mathrm {log}\): Base 10 logarithm

1.4. NOTES

The element results must be stored for Outmod in Calculation Parameters → Dynamic Calculation → Storage.
The stored effective tension is used instead of the axial stress resultant (true wall tension) in the fatigue analysis. This will normally not have a significant influence on the fatigue since the damage is calculated from the cycles. This may not ne the case if the inner or outer pressure acting on the cross section has large variations.