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Fatigue analysis
The basic assumption is the Miner rule for which the damages relative to different sea-states may be added to on another. The resulting global damage is the inverse of the Lifetime. The damage of each sea-state is evaluated from the stress or tension range distribution with respect to a given SN or TN curve.
Example for stress fatigue (S-N curves):
The fatigue cycles may be represented by the basic S-N curve given as :
where
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\(\Delta\sigma\) = stress range (MPa)
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\(N\) = predicted number of cycles to failure under stress range Ds
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\(log(\bar{a})\)= intercept of \(log(N)\) axis
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\(m\) = inverse slope of the \(S-N\) curve
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\(SCF\) = stress concentration factor
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\(t_{ref}\) = reference thickness
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\(t\) = thickness through which a crack will most likely grow. \(t = t_{ref}\) is used for thickness less than \(t_{ref}\)
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\(k\) = thickness
Using the Palmgren-Miner rule, the long-term damage is calculated from the short-term damages associated to each stress range level (called stress block I):
where
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\(n_i\) = number of stress cycles for stress block \(i\)
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\(N_i\) = number of cycles to failure at constant stress range (\(SCF*\Delta \sigma\)) for stress block \(i\)
It comes:
where
\(\Delta\sigma_i\) = stress range of stress block \(i\)
On one year, we have:
with
\(p_i\) = probability of occurrence of stress block \(i\) (derived form the stress distribution law)
\(T_{z,i}\) = apparent period associated to stress block \(i\)
The stress range distribution (stress level and associated number of cycles) is derived from former time domain simulations, either through the spectral or the Rain-Flow counting method. The first approach is based on the stress spectrum and therefore called the spectral approach. The second method relies on direct computation of cumulative damage associated with each semi-cycle and is called the Rainflow counting technique. Both approaches are currently used in the offshore industry to determine the fatigue life of steel risers for instance.
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Spectral : The spectral method has the advantage of being far less expensive in terms of CPU requirements and time than the Rainflow method. This method however rely on the assumption that the dynamic stress amplitude in the structure is more or less a linear function of the wave height. This method is widely used and is considered to be slightly conservative.
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Rainflow : The Rainflow counting technique is expensive but provides reliable damage estimates results. For this reason, the Rainflow counting is most of the time used to check the validity of the results obtained through spectral approach.
