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Fatigue analysis: S-N and T-N curves |
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Fatigue analysis: S-N and T-N curves |
An S-N curve defines the number of cycles to failure, $N(S)$, when a material is repeatedly cycled through a given stress range $S$. OrcaFlex uses the S-N curve to calculate the damage in a fatigue analysis. If needed you can define a number of different S-N curves and use them at different arc lengths along a line.
With each S-N curve you must also specify an associated stress endurance limit, $F_\mathrm{L}$, which is the stress range below which no damage occurs.
The S-N curve itself can be specified either by parameters or by a table.
To specify the curve by parameters, you define parameters $\logcom(a)$ and $m$; the curve is given by either of the following equivalent formulae \begin{equation} \begin{aligned} N &= aS^{-m} \\ \logcom N &= \logcom a - m \logcom S \end{aligned} \end{equation} The curve is either linear or bilinear, depending on the value of region boundary. If this is infinity the curve is linear; otherwise it is bilinear.
A bilinear curve, is specified by parameters $\logcom a_1$, $m_1$ for the low-cycle region $(N \leq \textrm{region boundary})$ and $\logcom a_2$, $m_2$ for the high cycle region $(N \gt \textrm{region boundary})$. Because the curve must be continuous, the value of $\logcom a_2$ is determined by $\logcom a_1$, $m_1$, $m_2$ and the region boundary. Hence $\logcom a_2$ is reported, but cannot be modified. The bilinear S-N curve is thus given by \begin{equation} \logcom(N) = \begin{cases} \logcom a_1 - m_1 \logcom S & \text{if $N \leq$ region boundary} \\ \logcom a_2 - m_2 \logcom S & \text{if $N \gt$ region boundary} \end{cases} \end{equation} To specify the curve by a table, you give a table of pairs of values of $S$ and $N$. For other values of $S$ we use log-linear interpolation or extrapolation to find the corresponding value of $N$.
Mean stress effects can be accounted for, if required, by selecting one of the available models.
The S-N curve entered must be consistent with the fatigue analysis units. S-N curve data are typically quoted with stress in MPa, but what if your fatigue analysis uses some other stress units? You can handle this as follows. Change the fatigue analysis units and set the units system to be user, the length units to be m and the force units to be MN. This corresponds to stresses in MPa, so you can now enter the S-N data in terms of MPa. Finally, restore the units to those that you want for the fatigue analysis. The S-N data (either parameters or tabular) will automatically be converted to the new units.
For mooring fatigue, damage is calculated from T-N curves. These define the number of cycles to failure, $N(T)$, when a material is repeatedly cycled through a given effective tension range $T$.
The T-N curve can be specified either by parameters or by a table.
To specify the curve by parameters, you give three parameters, $m$, $k$ and the reference breaking strength (RBS); the curve is given by \begin{equation} N = k\left(\frac{T}{\textrm{RBS}}\right)^{-m} \end{equation} To specify the curve by a table, you give a table of pairs of values of $T$ and $N$. For other values of $T$ we use log-linear interpolation or extrapolation to find the corresponding value of $N$.