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Plot the graph between **Stress (MPa)** and $\log(N)$ to study the fatigue behaviour.
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### Solved Numerical Example
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Given
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Force
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$$
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F = 24\ \text{N}
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$$
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Stress
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$$
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S = 49.67\ \text{MPa}
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$$
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Cycles
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$$
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N = 166560
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$$
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Therefore,
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$$
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\log(N) = \log(166560) = 5.222
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$$
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For the summary graph, the plotted point for this final stage is
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$$
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(\log(N), S) = (5.222,\ 49.67)
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$$
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which is plotted on the S-N curve.
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### Interpretation of Results
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- Higher stress generally produces lower fatigue life.
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- Lower stress generally increases the number of cycles to failure.
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- The S–N curve is used to estimate the expected service life of engineering components subjected to cyclic loading.
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### Result
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The fatigue behaviour of the given specimen is studied by determining the relationship between applied stress and number of cycles to failure using the S-N curve representation shown in the simulation.
"question": "1. A rod with cross-section area of 3.22 cm<sup>2</sup> is subjected to static mean tensile load of 44.5 kN. What fatigue stress amplitude σ<sub>a</sub> will produce failure after 106 cycles? Assume σ<sub>n</sub> = 220.6 kN/m<sup>2</sup> , σ<sub>u</sub> = 415 kN/m<sup>2</sup>.",
"b": "Incorrect. Fatigue life depends strongly on the applied stress amplitude.",
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"c": "Correct. Increasing the stress amplitude generally reduces the number of cycles to failure.",
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"d": "Incorrect. Increasing stress does not produce infinite fatigue life."
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},
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"correctAnswer": "c",
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"difficulty": "intermediate"
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},
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{
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"question": "5. The S–N curve relates the applied stress to the ____.",
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"answers": {
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"a": "Specimen diameter",
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"b": "Number of cycles to failure",
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"c": "Young's modulus",
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"d": "Temperature"
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},
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"explanations": {
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"a": "Incorrect. Specimen diameter is not represented on the S–N curve.",
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"b": "Correct. The S–N curve shows the relationship between stress and the number of cycles to failure.",
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"c": "Incorrect. Young's modulus is not obtained from the S–N curve.",
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"d": "Incorrect. Temperature is not plotted on the S–N curve."
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},
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"correctAnswer": "b",
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"difficulty": "intermediate"
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},
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{
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"question": "6. The endurance limit of a material represents the stress below which the material can withstand ____.",
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"answers": {
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"a": "Only one loading cycle",
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"b": "A specified impact load",
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"c": "An indefinitely large number of loading cycles without failure",
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"d": "Only compressive loading"
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},
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"explanations": {
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"a": "Incorrect. The endurance limit is not related to a single loading cycle.",
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"b": "Incorrect. Impact loading is unrelated to the endurance limit.",
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"c": "Correct. The endurance limit is the maximum stress below which fatigue failure does not occur even after an indefinitely large number of cycles.",
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"d": "Incorrect. The endurance limit is not restricted to compressive loading."
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},
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"correctAnswer": "c",
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"difficulty": "intermediate"
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},
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{
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"question": "7. Fatigue failure generally occurs due to the ____.",
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"answers": {
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"a": "Instantaneous yielding of the entire specimen",
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"b": "Gradual initiation and propagation of cracks under cyclic loading",
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"c": "Melting of the material",
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"d": "Sudden increase in temperature"
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},
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"explanations": {
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"a": "Incorrect. Fatigue failure is progressive rather than instantaneous.",
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"b": "Correct. Fatigue failure occurs through crack initiation followed by gradual crack propagation until final fracture.",
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"c": "Incorrect. Melting is unrelated to fatigue failure.",
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"d": "Incorrect. Temperature alone does not define fatigue failure."
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},
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"correctAnswer": "b",
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"difficulty": "advanced"
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},
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{
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"question": "8. Which of the following generally improves the fatigue life of a component?",
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