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When a crack has been initiated in a material, further loading of the material causes stress concentrations at the crack tip. This high stress causes the material to break at the tip and the crack grows. As the material is loaded again, another stress concentration occurs and the crack grows again. But why do we need to unload the material in between? Why doesn't the crack just propagate immediately from the initial notch?

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    $\begingroup$ Depends on the material and direction of the crack, cyclic fatigue is a whole new topic... $\endgroup$ – Solar Mike Mar 19 at 18:08
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    $\begingroup$ If the load fractures it it is a fracture. If the load does not fracture it , it is a fatigue cycle. There may or may not . be more fatigue cycles . $\endgroup$ – blacksmith37 Mar 19 at 19:48
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    $\begingroup$ @blacksmith37 this is a good read: aviation-safety.net/database/record.php?id=19540110-1 $\endgroup$ – Solar Mike Mar 19 at 20:37
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    $\begingroup$ Apparently an older report. That was the second Comet failure , I think the first was over/near Iran , same cause. Fatigue of not very tough aluminum window frames with square corners . Cracks started there and propagated. The first crash analysis had not been finished when the second happened. The end of Comets and the beginning of rounded windows. $\endgroup$ – blacksmith37 Mar 20 at 0:53
  • $\begingroup$ On the net I found Comets did fly for some years with rounded windows and other changes. $\endgroup$ – blacksmith37 Mar 22 at 20:29
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When the material "breaks", it's the inter-molecular bonds that are breaking. Once they are able to form a new bond to the next available molecule the crack propagation stops and stress is reduced.

Once the load is removed, the material is deformed slightly from it's previously unloaded state. Adding load again creates a similar stress compared to the first load cycle causing another cycle of fracture.

Look up brittle vs ductile fracture, those sources will explain why some materials fail instantly while others fail after high number of cycles.

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