1. S-N curve

1.1. Purpose

Input for S-N curve used for fatigue analysis.

1.2. Basic theory

The basic form of the S-N curve given in recommended practice DNVGL-RP-0005:2014-06 is as follows:

\[logN = log\bar{a}-mlog\Delta\sigma ,\]

where

  • N = predicted number of cycles to failure for stress range \(\Delta\sigma \)

  • \(\Delta\sigma\) = stress range

  • m = negative inverse slope of S-N curve

  • \(log\bar{a}\) = intercept of log N-axis by S-N curve

Note the following:

  • The base 10 (or common) logarithm is normally used in standards.

  • The intercept of the log N-axis depends on the unit in the S-N curve. MPa is chosen as unit in the DNV recommended practice, but other units may be used elsewhere.

  • The program uses the intercept of the y-axis (stress range)as input. An example of how this is calculated is given below.

Thickness may be accounted for by modifying the design S-N curve for thickness larger than the reference thickness:

\[logN = log\bar{a}-mlog(\Delta\sigma((\frac{t}{t_{ref}})^{k})),\]

Where:

  • \(t_{ref}\) = reference thickness

  • k = thickness exponent on fatigue strength

1.3. Predefined S-N curves

If the Use Predefined curve option is selected, an S-N curve can be selected from the drop down list. The reference thickness factor is the ratio of base material thickness and reference thickness (\(\frac{t}{t_{ref}}\)). This factor should normally be larger than 1.0. A default thickness exponent is used. To inspect and edit the resulting input, select Use values in editable version.

1.4. Direct input of S-N curves

The S-N curves are defined using the following input:

  • Negative inverse slope (of first segment)

  • Intercept stress, stress range resulting in failure after one cycle. This is the Y-intercept of the first segment.

  • Reference thickness factor, the ratio of thickness and reference thickness (\(\frac{t}{t_{ref}}\))

  • Thickness exponent, thickness exponent on fatigue strength (k)

  • Negative inverse slope of next segment (m)

  • Transition point between given and previous segment, logarithm of cycles at transition.

Note that the \(log\bar{a}\) (X-intercept) is calculated in MPa and shown to the user for reference.

1.5. Calculating intercept stress

The basic form of the S-N curve is:

\[ logN = log\bar{a}-mlog\Delta\sigma\]

The intercept stress is the stress range resulting in failure after one cycle (logN =0). The intercept stress is then calculated as follows (assuming base 10 logarithm):

\[ 10^{\frac{log\bar{a}}{m}}\]

For DNV B1 curve in air this results in :

\[ 10^{\frac{15.117}{4.0}} = 6015.199005 (MPa)\]

Note the unit of the resulting intercept stress as DNV curves are in MPa. If units in the workspace are set to m/N, the stress must be multiplied by 1e+06 to convert to Pa before entering the value as intercept stress.

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