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It is a little difficult to find a simple example of fatigue. For most common items, there is no investigation into the cause of failure so we don't know what caused it. We simple through the part away and get another one. If the pedal on our bicycle breaks, we just throw it away and get a new one; no questions asked. The earliest example of fatigue failure is the failure of an axle. There are some much early examples but even going back to the beginning of the 20th Century, there were some train crashes that was due to failure of the axle or the axle-to-wheel joint. This is a common example because an axle is a long rod that is bent. So as the train rolls, the axle is bent one direction and then the opposite as it revolves. A train can travel for hundreds of miles and thousands upon thousands of revolutions. Also, the early axle/wheel designs had sharp corners that also contributed to fatigue failure as it raises the stress at the joint. I find another example of fatigue laying on the street. If you look around you will find lug nuts from a car's wheel. It will have the lug nut and the stud that it was threaded on both together. The stud will be broken and inside the nut. The fracture surface of the stud or lug will have features that signify a fatigue failure. You may have to inspect it under a 10X magnifying glass to see this (or ask an engineer to show you). This failure of the lug nut experience a fatigue failure either because of repeated torquing of the nut when installing the wheel OR by the same factors as described about the train axle/wheel failures. Maybe the wheel is warped and it is applying high repeated loads to the lug nut. This is a practical example but may require someone who can identify it as a fatigure failure. Some websites will give as a simple example of fatigue failure is the bending of a paper clip or a wire coat hanger. This is NOT FATIGUE. When you bend a paper clip or coat hanger back and forth you are Yielding the part or deforming it permanently. Loads that produce fatigue failure do not bend the part; the load just applies stress and then relieves the stress. When you bend a coat hangar back and forth you may feel heat at the bend---that indicates the properties of the metal is being affected by other means. This is not Fatigue.

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Q: Pratical example of fatigue
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