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Fatigue curves file format for fatigue analysis

The fatigue curves used for riser fatigue calculation are S-N curves given as:

\[ \log(N) = log(A) - m\log\Bigl(\Delta\sigma \Bigl(\frac{t}{t_{ref}}\Bigr)^k\Bigr) \]

Ds is the stress range in \(MPa\)

\[ N = 10^{\log(N)} \]

The fatigue curves used for mooring fatigue calculation are T-N curves given as:

\[ \log(N) = log(K) - M \log \Bigl( \frac{\Delta T}{MBL} \Bigr) \]

DT is the tension range MBL is the Minimum Breaking Load DT and MBL must be defined in the same unit

For S-N curves, the fatigue curves files extension is .CSN. Three parameters are defined: log(A), m, Dscutoff

For T-N curves, the fatigue curves files extension is .CTN. Three parameters are defined: K, M, DT/MBL limit

The definition principle is described on the following graph:

The fatigue curve is defined from right hand to left hand. For each segment, 3 parameters are given:

Ds m constant

If no cut-off value exists below which stress range levels do not contribute to fatigue damage, the first segment cut-off value Ds must be 0.

If a cut-off value exists below which stress range levels contribute to fatigue damage, for example in case of sufficient cathodic protection, the cut-off level of the first segment must be equal to the cut-off level of the second segment.

Example of one slope S-N fatigue curve parameters:

SN_FATIGUE_CURVE_NAME
1
0. 3.0 11.824

This means that the curve inverse slope m is 3 and the constant log(A) is 11.824, no limit below which stress range levels do not contribute to fatigue damage.

Example parameters for a two slopes S-N fatigue curve without fatigue endurance limit:

SN_FATIGUE_CURVE_NAME
2
0.0 5.0 15.606
83.4 3.0 11.764

This means that:

m = 5 and log(A)=15.606 for 0.0 MPa <= Ds <= 83.4 MPa, m = 3 and log(A)=11.764 for Ds > 83.4, i.e. N <= 10E6

Example parameters for a two slopes S-N fatigue curve with fatigue endurance limit:

SN_FATIGUE_CURVE_NAME
3
0.0 0.0 15.606
23.8 5.0 15.606
83.4 3.0 11.764

This means that:

There is no failure for Ds <= 23.8 MPa, m = 0 and log(A)=15.606 for Ds <= 23.8 MPa
m = 5 and log(A)=15.606 for 23.8 MPa <= Ds <= 83.4 MPa, i.e. 10E6 <= N <= 5.286 10E8
m = 3 and log(A)=11.764 for Ds > 83.4, i.e. N <= 10E6

It corresponds to the following graph:

Example of T-N fatigue curve parameters:

TN_FATIGUE_CURVE_NAME
1
0 3.36 370

This means that the curve slope M is 3.36 and the constant K is 370.

The file structure is as follows:

For i =1 to Maximum number of fatigue curves<br>
    Curve name<br>
    Number of slope(s)<br>
    For j =1 to Maximum number of slopes<br>
CUTVALUE M CONST<br>
    End for j<br>
End For i<br>

CUTVALUE Stress range value in MPa for the ith level in case of SN curve or DT/MBL limit in case of TN curve
M Coefficient m of a SN curve (inverse slope), coefficient M of a TN curve
CONST log(A) for a SN curve, K for a TN curve

Example of S-N curves file:

DNV-B1-air
2
0. 5.0 16.856
93.58 3.0 12.913
DNV-B2-air
2
0. 5.0 16.566
81.88 3.0 12.739
DNV-C-air
2
0. 5.0 16.32
73.11 3.0 12.592
DNV-C1-air
2
0. 5.0 16.081
65.49 3.0 12.449
DNV-C2-air
2
0. 5.0 15.835
58.48 3.0 12.301
DNV-T-air
2
0. 5.0 15.606
52.63 3.0 12.164

Example of T-N curves file:

API-common-chain-link
1
0. 3.36 370
API-Baldt_Kenter
1
0. 3.36 90
API-Multi-strand-rope
1
0. 4.09 231
API-Spiral-strand-rope
1
0. 5.05 166

Warning

The thickness effect coefficients (k, tref) are not defined in the fatigue curves files. Then, SCF coefficients seized in the riser model segment types, must include the equivalent SCF due to thickness effect, according to the thickness effect factor and the reference thickness associated to the fatigue curve.

Note

T-N curve K and M coefficient may be derived from one S-N curve coefficients, the minimum breaking load MBL and the material cross section area \(S_{mat}\). One has:

\(N = \frac{K}{(\frac{\Delta T}{MBL})^M}\) and \(N = \frac{A}{(\Delta\sigma)^N}\) with \(\Delta\sigma\) in \(MPa\)

It comes: \(K = A\frac{S_{mat}}{MBL}^m\) and \(M\) = \(m\)

\(\Delta\sigma\) , \(S_{mat}\) and \(MBL\) units must be consistent:

\(\Delta\sigma\) in \(MPa\), \(MBL\) in \(N\) and \(S_{mat}\) in mm2

or \(\Delta\sigma\) in \(MPa\) \(MBL\) in \(MN\) and \(S_{mat}\) in m2