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Define Fatigue - Materials
The normative view of the stress/strain is found in the example of the paper clip wire experiment. Take a paper clip wire and try to break it by pulling on it by hand. You are unable to break it because you need to exceed the ultimate stress of the material. Bend a paper clip between your fingers and the following is observed: when the wire rebounds to its original shape the proportional/elastic limit is observed; bend it farther to a point where the wire is permanently deformed, the yield point is observed; and, when the wire is bent one way then the other a few times, the wire breaks easily. The phenomenon is known as fatigue.
All materials have microcracks. The cracks are not critical and are averaged as ultimate strength for the bulk material in a tension test. However, when the material is subjected to cyclic loading, the microcracks can grow until some of the cracks reach critical length, at which time the material breaks. The stress value at cyclic loading is significantly lower than ultimate stress of the material. Failure due to cyclic loading at stress levels significantly lower than the static ultimate stress is called fatigue. All engineered systems account for fatigue failure. At low levels of stress the failure may occur at millions or billions of cycles. Endurance tests determine the cyclic loadings and fatigue strength.
Exponential distribution - Poisson distribution function: Let X follow exponential distribution with parameter θ. Find the pdf of Y = X 1/β where β( ≥ 1 ) is a constant.
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