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The S-N curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit?

S-N curve of fatigue strength S against number of cycles N, falling from Sut through points 1, 2 and 3 and levelling off at point 4

  • A.\(S_{ut}\)
  • B.\(S_{2}\)
  • C.\(S_{3}\)
  • D.\(S_{4}\)

Answer: D

The endurance limit is \(S_{4}\).

For steel, the S-N curve falls as the number of cycles rises and then levels off into a horizontal line, here from point 4 at about \(N_{4}\) cycles onward. The stress at that horizontal part is the endurance limit: a specimen loaded below it can survive an unlimited number of cycles.

\(S_{ut}\), where the curve meets the stress axis, is the ultimate tensile strength, the stress that breaks the specimen in a single loading. \(S_{2}\) and \(S_{3}\) are fatigue strengths at finite lives \(N_{2}\) and \(N_{3}\): the specimen fails after that many cycles, so they are not limits below which life is unlimited.

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