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S-N curves

In order to set a suitable design criteria, I am looking to compare two classes of S-N curves for a fatigue design, viz., E and F2, and I cannot not find a handy plot to refer to, and it is frustrating when standards fail to include. So, I channel it to write some code to roll my own:

S-N curves

The basic S-N curve equation is as follows, which one may know is from Paris-Erdogan law (fracture mechanics):

\begin{aligned} N = k_1 \cdot S^{-m} \newline \end{aligned}

The standard does describe it in its logarithmic form, which is as follows:

\begin{aligned} \log N = \log k_1 - m \cdot \log S \newline \end{aligned}

and then it goes on to furnish its two sets of key components that form parts of the equation — highlighted below.1

From ISO 19902:2007


  1. Playing with logarithms is fraught with error, as they are not the same as plain algebra — Leonhard Euler’s gift to the world, which reminds me I should jog my memory from high-school. There is a very nice podcast recording (mp3) on Euler’s e that also discusses the history of logarithms, which was in ancient days allowed to transform “complicated” multiplication into simple addition, which makes perfect sense in a world that had no computers, no calculators, and no slide rules.