Bend a paperclip back and forth a few times. It will eventually break. This is known as a fatigue failure: the repeated stress (below fracture stress) that causes a material to fail. Most materials will fail due to fatigue stresses at some point; in fact, an estimated 90% of materials failures involve a fatigue related failure. Another good example is the Tacoma Narrows Bridge: it was placed under stress everytime the wind blew, and some took it for granted. One day, the critical fatigue value, N, was reached, and the bridge fell into the water.

As I mentioned above, most materials will fail from fatigue at some point: If you tap on the Hoover Dam with your finger enough times, it will fail, though your finger bone will be more likely to fail first. Some materials, particularly some steels, this is not the case. There is a minimum stress to start fatiguing the material, and below it, you can stress that amount an infinite number of times before it fails.

Unfortunately, there is no way to predict how much stress will be applied at any given time. We would like to believe that stuff acts as a constant force or as a sinusoid (i.e. the paperclip is theoretically a sinusoidal example). However, for most practical engineering applications, this is not the case; wind does not behave as either of these, as it is constantly changing to a seemingly random value at any given time. Some processes we have machined almost perfect: i.e. the crankshaft in your car will almost always move as a sinusoid. Not quite a perfect one, however.