## 31 Aug S-N Curves

When conducting a stress based fatigue analysis (https://fea-solutions.co.uk/stress-based-fatigue-analysis/), the S-N curves of the materials used are required, where S stands for σ (sigma), the symbol for stress, and N for the number of loading cycles with the graph showing the mean stress over the number of cycles required for the component to fail. S-N curves are also known as Wöhler’s Curves.

For steel, the S-N curve could have two distinct sections. One is where the stress is decreasing as the load cycles increases. The other is where the graph becomes horizontal, that means the stress required for fatigue failure is constant independent of the number of load cycles. The latter is called the Endurance Limit (https://fea-solutions.co.uk/endurance-limit-analysis/) of the material. When using a logarithmic scale on both axes, each of the two parts of the graph are straight lines.

If the endurance limit is not known, the fatigue ratio of the material can be used, which is the ratio of the endurance limit to ultimate tensile strength (UTS). The fatigue ratio multiplied by the UTS is an approximation for the endurance limit. Using the approximation that the fatigue strength of the material is a given value of the UTS at 1000 load cycles (for steels this is 0.9 x UTS), this point can, in a logarithmic graph, be joined by a straight line to the endurance limit of the material, thus completing the S-N curve.

It must be noted that although S-N curves can be approximated, this is only very generalised and thus should be used with caution when conducting anything other than preliminary fatigue analyses.

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