Fatigue Failure and Endurance Limit Questions and Answers

Answer: C

The S-N curve shows the relation between stress amplitude and the number of cycles to failure. It is plotted from fatigue tests at different stress levels and is used to find the endurance limit. The stress intensity factor belongs to fracture mechanics, strain amplitude is used in low cycle fatigue (the strain-life curve), and elastic modulus is a constant property of the material, so the other options are wrong.

On the S-N curve the stress amplitude is plotted against the number of cycles on a logarithmic axis, and for steels the curve flattens at the endurance limit.

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.

Answer: A

The most conservative approach is the Soderberg line.

On a plot of alternating stress against mean stress, each criterion draws a boundary from the endurance limit on the alternating-stress axis to a point on the mean-stress axis. The Soderberg line runs to the yield strength, the Modified Goodman line to the ultimate strength, and the Gerber curve is a parabola through the ultimate strength. Since yield strength is lower than ultimate strength, the Soderberg line lies inside the other two and allows the smallest stresses, making it the most conservative.

The Gerber parabola is the least conservative of the three. The yield (Langer) line guards against first-cycle yielding, not against fatigue, so it is not a fatigue failure criterion on its own.

Answer: B

The maximum stress is half of the endurance limit.

Loading in tension and unloading gives a repeated cycle from 0 to \(\sigma\), so \(\sigma_{a} = \sigma_{m} = \sigma/2\). Soderberg's line with factor of safety N reads \(\sigma_{a}/S_{e} + \sigma_{m}/S_{y} = 1/N\). With \(S_{e} = S_{y}\):

\[ \begin{aligned} \frac{\sigma/2}{S_{e}} + \frac{\sigma/2}{S_{e}} &= \frac{1}{2} \\ \sigma &= S_{e}/2 \end{aligned} \]

The ultimate strength plays no part in Soderberg's criterion, which uses yield. One-fourth applies the factor of safety twice, the endurance limit itself ignores it, and twice the endurance limit exceeds the yield strength.