Things break at loads they survived a thousand times

How repeated loading accumulates damage that a single load does not.

A part can carry a given load without any trouble a thousand times over and then fail on the thousand-and-first identical cycle, because each repetition leaves behind a small amount of permanent damage that never heals between cycles and simply keeps adding up until there is enough of it to finish the part off.

Petroski's To Engineer Is Human makes the case that engineering advances mainly through failure, and that successful designs teach almost nothing, a claim that reads as needlessly bleak the first time through and starts to feel obviously true the moment a part that has passed every test finally fails for a reason nobody thought to test for.

What is really going on

A single load, applied once, is judged against a part's strength, and if the part is stronger than the load, that is normally the end of the story. Repeated loading changes the question entirely, because a load well below the part's strength can still be doing something to the material every time it is applied, even though nothing about the part's overall shape or size changes and even though the load itself never gets any closer to what would be needed to break the part outright in a single go. That something is a tiny amount of permanent, localised damage forming at whichever point in the part is under the most stress, and unlike a dent that can be massaged back into shape or a bruise that fades, this particular kind of damage does not reverse itself between cycles. It simply sits there, waiting for the next cycle to add a little more, and a part can carry an enormous number of cycles this way, feeling and testing exactly as strong as new right up until the accumulated damage finally reaches the point where it takes over from the rest of the part entirely. This is what makes the failure feel sudden to whoever is standing nearby when it happens, even though nothing about it actually was sudden, since the part had been quietly working toward that exact moment for its entire working life, only ever showing the evidence at the very end rather than gradually along the way.

The flip-flop-strap comparison

A rubber flip-flop's toe strap survives every single step of an ordinary walk without the faintest sign of strain, since one footstep's worth of force is nowhere near what the strap is capable of carrying, and if a wearer judged the strap purely by how it handled that one step, it would look essentially indestructible. Months later, often without any single dramatic moment of overloading it, that same strap tears clean through at the exact point where it loops through the sole, not because a step finally arrived that was harder than all the ones before it, but because every one of those thousands of earlier, perfectly ordinary steps left behind a trace the rubber never fully recovered from. The strap did not get weaker gradually in a way a person could feel underfoot along the way, it stayed apparently fine until the accumulated damage reached its limit, and then it simply let go, usually at the least convenient possible moment. A brand new strap bought as a replacement will happily survive the identical walk to the shop and back that finally broke the old one, which is the clearest possible demonstration that the failure was never about the size of any single step, it was about how many of them the strap had already been asked to absorb before that particular walk began.

Why damage from repeated loading never heals between cycles

The reason this accumulation happens at all comes down to what is occurring at a scale far too small to see: repeated loading, even well below a material's overall strength, can still rearrange a tiny cluster of the material's internal structure at whichever spot happens to be carrying the highest local stress, and that rearrangement is a genuinely permanent change rather than a temporary strain that relaxes back once the load is removed. Wikipedia's overview of fatigue in materials describes this as damage accumulating cycle by cycle until a crack initiates and grows, and the crucial detail is that none of this reverses during the parts of the cycle when the load is removed, the way a spring returns to its original length once released. Each cycle instead adds its own small, permanent contribution on top of whatever was already there from every cycle before it, which is exactly why a part's fatigue life has to be measured in a number of cycles survived, not in a single strength number the way an ordinary one-off load is judged.

The number that matters here

A material's fatigue strength, the highest repeated stress it can go on surviving cycle after cycle without ever failing, commonly comes out at only a fraction of that same material's one-time static strength, often somewhere in the region of half for many ordinary metals, which is why a part sized comfortably against the single largest load it is ever expected to see can still be carrying an everyday repeated stress that sits well inside the danger zone for fatigue, despite being nowhere close to the load that would actually break it in one go.

What this changes in practice

Judging a part only against the single largest load it is ever expected to see, the way a simple strength calculation naturally does, misses this entire category of failure, since a part can pass that check comfortably and still be counting down toward a fatigue failure driven by loads far smaller than the one the calculation checked. The practical consequence is that any part expected to carry a repeated load, which in practice is most moving machinery, needs its lifetime measured in cycles as well as its strength measured in force, and the two numbers answer genuinely different questions rather than being two ways of asking the same one. A part can be strong and still be short-lived, and the gap between those two properties is exactly what the rest of this set works through, starting with the fact that the damage itself does not accumulate smoothly either, but grows through two quite different phases on its way to a final break.