S-N Curves of Materials in Fatigue Calculations

S-N Curves of Materials in Fatigue Calculations

In structural and mechanical design, Fatigue calculations are very important to estimate when and where the designed part will fail. So, in fatigue calculations, S-N curves are used to predict the failure of the material below the ultimate strength values and stresses. Here, we explain the S-N curves. 

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What is S-N Curve?

S-N curve of materials.
The S-N curves of aluminum alloys(Image Source: Steven R. Schmid, Bernard J. Hamrock, Bo O. Jacobson – Fundamentals of Machine Elements, 3rd Ed., Pg: 166).

Firstly, S-N curves are the plottings where several cycles and the fatigue stress levels that they show. You can find the estimated corresponding number of cycles of the stress levels from these curves of materials.

We also call them Wöhler Diagrams named after a German engineer August Wöhler who published his first fatigue research in 1870.

How to Obtain These Curves?

And also, they plot the S-N curves with the rotating beam experiments. In rotation beam experiments, we use a standard beam. And we load with pure bending. And then, we rotate the beam under these bending conditions up to failure. This pure bending load is below the yield strength of the material. By the rotation of the test specimen, we obtain cyclic pure bending loading. So, they are logging into the graphics up to which cycles that this test specimen will endure. These graphs are the S-N curves of the specimens. 

Endurance Limits on S-N Curves

In some of these curves of materials, there is a limit which we call an endurance limit. Cyclic stress levels are below the endurance limits of materials, that material will not fail because of fatigue. So, below this level, we can apply an infinite number of cycles to the part. Furthermore, not all the materials are showing endurance limits on S-N curves. 

Which Materials Have Endurance Limits?

Endurance limits.
You can see the exact endurance limit of steel(Image Source: Wikimedia.).

In general ferrous materials and titanium alloys are showing straight endurance limits. And such materials as aluminum alloys, copper, and magnesium are not showing any straight endurance limits in their S-N curves. 

But the prediction of the endurance limits for materials is not an easy thing. We require lots of kinds of experiments that may predict endurance limits. Once we define the endurance limits of materials, we can produce safe structures in terms of fatigue. 

Endurance Limits of Steels

There is a prediction formula for the endurance limits of steel. With the different loading conditions, different kinds of endurance limits can be calculated. 

  • In the bending load, the endurance limits of general streels are approximately 0.5xUltimate Strength. 
  • In the axial load, which may occur as compression or tension, the total endurance limit can be calculated as 0.4xUltimate Strength. 
  • In the torsional loading conditions on steels, the approximate value of the endurance limit can be calculated as 0.30x Ultimate Strength. 

For some materials, there are no data to show all the S-N curve diagrams with changing load stresses. Research and development institutions, obtain these curves. And also endurance limits may be specified to use in such applications. 


So, these are the general information about the S-N curves of materials in fatigue calculations. 

Finally, do not forget to leave your comments and questions below about these curves in fatigue calculations.

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