1. Time domain S.N fatigue damage

This option allows for calculation of fatigue damage calculation from axial and bending stresses in circular metallic homogeneous risers using a specified SN curve and rainflow cycle counting.

The calculated fatigue damage is per year of the specified environmental conditions.

The fatigue damage is calculated based on the stored force time series from DYNMOD (see data group File storage for internal forces for storage information) and the component properties specified in INPMOD. Stresses may only be calculated for CRS1 and CRS0 components.

The fatigue damage is calculated for a specified number of points on the tube circumference.

1.1. Data group identifier, one input line

TIMEdomain FATIgue DAMAge       NoPlot

1.2. Control data, one input line

NSECT NPCS IOPPR TBEG TEND IOPSTR FAT-ID

  • NSECT: integer: Number of riser cross sections to be considered

    • NSECT = 0: All cross section where forces are available is included in the analysis

  • NPCS: integer: Number of points in the cross section where fatigue is calculated

  • IOPPR: integer: Print option for fatigue results

    • IOPPR = 0: Print results only for most critical point in cross section

    • IOPPR > 0: Print results for all NPCS points

  • TBEG: real >= 0, default: 0: Beginning of interval for fatigue calculation \(\mathrm {[T]}\).

    • The default is the first time step in the stored force time series.

    • Must be less than the simulation length.

  • TEND: real >= 0, default: 0: End of interval for fatigue calculation \(\mathrm {[T]}\).

    • The default is the last time step in the stored force time series.

    • If the specified value is larger than the length of the stored force time series, it will be set to the the last time step in the stored force time series.

  • IOPSTR: integer, default: 0: Option for stress calculation

    • IOPSTR=0: Bending stresses calculated from bending moment (recommended)

    • IOPSTR=1: Bending stresses calculated from curvatures. EMOD and DIAST must be given

  • FAT-ID: character(16): Identifier for fatigue calculation. Used in result presentation only

The remaining of the time series is used if TEND is less or equal to TBEG (Default is full time series).

1.3. Cross-sectional data, one input line

DSCFA DSCFY DSCFZ ASI WSTI DIAST EMOD CFRS LFRS TEFF

  • DSCFA: real, default: 1: Default stress concentration factor for axial force contribution

  • DSCFY: real, default: DSCFA: Default stress concentration factor for bending about the local Y axis

  • DSCFZ: real, default: DSCFA: Default stress concentration factor for bending about the local Z axis

  • ASI: real, default: See below: Optional cross-sectional area \(\mathrm {[L^{2}]}\)

  • WSTI: real, default: See below: Optional section modulus \(\mathrm {[L^{3}]}\). Dummy if stresses are are calculated from curvature (IOPSTR = 1)

  • DIAST: real, default: See below: Cross section diameter. Used to calculate stresses from curvature if IOPSTR = 1. Otherwise not used.

  • EMOD: real, default: See below: Modules of elasticity. Used to calculate stresses from curvature if IOPSTR = 1. Otherwise not used.

  • CFRS: real, default: 0: Constant correction coefficient, friction stress \(\mathrm {[FL^{-2}]}\)

  • LFRS: real, default: 0: Linear correction coefficient \(\mathrm {[L^{-2}]}\)

  • TEFF: real, default: See below: Effective thickness used together with the reference thickness TREF given below in thickness correction \(\mathrm {[L]}\)

The cross-sectional area, modulus and thickness defined for each cross section in INPMOD are used as defaults for ASI, WSTI and TEFF.

Stress range correction due to friction is given as:

\(\mathrm {\Delta \sigma _f=CFRS+LFRS\times T_{avg}}\)

\(\mathrm {T_{avg}}\) is the static value of the tension. The friction stress correction is added after Rainflow counting of the stress time series due to axial force and bending

\(\mathrm {\sigma _{tot}(t)=\sigma _{axial}(t)\times SCFA+\sigma _{Y-bending}(t)\times SCFY+\sigma _{Z-bending}(t)\times SCFY}\)

The units of the friction correction coefficients must be consistent with the Selection of unit system physical constant in INPMOD.

1.4. SN curve data, two input lines

Fatigue capacity curve description

NOSL LIMIND FATLIM RFACT TREF KEXP

  • NOSL: integer <= 5, default: 1: Number of straight lines defining the SN curve

  • LIMIND: integer, default: 0: Fatigue limit indicator

    • LIMIND < 0: Fatigue limit in terms of stress cycles is specified

    • LIMIND = 0: No fatigue limit for present curve

    • LIMIND > 0: Fatigue limit in terms of stress range is specified

  • FATLIM: real, default: 0: Fatigue limit, interpretation dependent on LIMIND. See Example 1 below.

    • LIMIND < 0: Base 10 logarithm of number of stress cycles for which the SN curve becomes horizontal

    • LIMIND = 0: FATLIM is dummy

    • LIMIND > 0: Stress range level for which the SN curve becomes horizontal \(\mathrm {[S]}\)

    • See RFACT below

  • RFACT: real, default: 1: Factor between the stress unit \(\mathrm {[S]}\) used to define the SN curve and the force and length units \(\mathrm {[F]}\) and \(\mathrm {[L]}\) chosen in INPMOD

    • \(\mathrm {S\times RFACT=\frac{F}{L^2}}\)

  • TREF: real, default: 0: Reference thickness for thickness correction \(\mathrm {[L]}\).

    • TREF = 0: No thickness correction

  • KEXP: real, default: 0: Exponent for thickness correction.

    • KEXP = 0: No thickness correction

If \(\mathrm {kN}\) and \(\mathrm {m}\) were chosen as force and length units while the SN curve is given in \(\mathrm {MPa}\), RFACT should be set to 0.001.

If the SI units \(\mathrm {N}\) and \(\mathrm {m}\) were chosen for force and length and the SN curve is in \(\mathrm {MPa}\), RFACT should be set to 1.0E-6.

um io fig325
Figure 1. Example 1: 2 segments and fatigue limit. Note that FATLIM can be alternatively specified
um io fig326
Figure 2. Example 2: 3 segments and not fatigue limit. Illustration of input data for fatigue capacity curve definition
TREF`and `KEXP must either both be zero, no thickness correction, or both positive, thickness correction included.

Fatigue capacity curve constants

RM1 RC1 RMi RNCi ...

  • RM1: real: Slope of the SN curve. First curve segment for NOSL>1, total curve for NOSL=1. (log cycles / log stress)

  • RC1: real: Constant defining the SN curve. First segment or total curve

  • RMi: real: Slope of curve segment i, i=2, …, NOSL

  • RNCi: real: Transition point between curve segment (i-1), and i, i=2,…, NOSL| (log cycles)

For a single slope SN curve, log cycles as a function of log stress:

\(\mathrm {N=C\times \Delta S^{RM1}}\)

or

\(\mathrm {logN=RC1-|RM1|\times log\Delta S}\)

Where:

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

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

  • \(\mathrm {C=10^{RC1}}\)

or log stress as a function of log cycles:

\(\mathrm {log\Delta S=\frac{RC1}{|RM1|}-\frac{logN}{|RM1|}}\)

1.5. Cross section specification, NSECT input lines

LINE-ID ISEG IEL IEND SCFA SCFY SCFZ

  • LINE-ID: character(8): Line identifier

  • ISEG: integer >= 0: Segment number on line

    • = 0: All segments in specified line

  • IEL: integer >= 0: Local element number on specified segment

    • = 0: All elements in specified segment

  • IEND: integer:

    • IEND = 0: Cross sections at both ends checked

    • IEND = 1: Cross section at end with smallest node number checked

    • IEND = 2: Cross section at end with largest node number checked

  • SCFA: real, default: DSCFA: Stress concentration factor for axial force contribution

  • SCFY: real, default: SCFA: Stress concentration factor for bending about local Y axis

  • SCFZ: real, default: SCFA: Stress concentration factor for bending about local Z axis

Time domain forces for the specified elements must be stored in DYNMOD, see data group File storage for internal forces for storage information.

If several specifications match an element, the first specification will be used.