Fatigue cracks grow slowly and then all at once
The two phases of crack growth, and why warning is so short.
A fatigue crack spends nearly the whole of its working life growing by an amount too small to see with each cycle of load, and only in its very last moments does it suddenly accelerate into the fast, unstable tear that actually separates the part, which is why a component that looked perfectly sound at the last inspection can still fail catastrophically before the next one arrives.
The mechanism behind two-stage crack growth
A fatigue crack does not grow at a constant rate for its whole life, it grows in two quite different phases that share almost nothing in common except that they happen to the same crack. The first phase begins once the accumulated damage described in the previous article has produced an actual microscopic crack, and from that point the crack advances a tiny, roughly repeatable distance with every single cycle of load, sometimes leaving faint growth bands behind that a careful inspection under magnification can actually count, one band for each burst of loading the part experienced. This stable growth phase can go on for the overwhelming majority of a part's fatigue life, the crack lengthening steadily but slowly enough that the part otherwise looks, feels and performs exactly as it always has. The second phase arrives only once the crack has eaten far enough into the part that whatever material remains around it can no longer carry the working load elastically, and at that point growth stops being steady and becomes explosive, the crack racing across the remaining cross-section in a process that has far more in common with an ordinary sudden overload fracture than with anything that came before it in the same part.
The torn-paper comparison
Anyone who has ever torn a sheet of paper starting from a small nick cut with scissors has already felt both of these phases directly. Pulling steadily on paper that carries a small starting nick tears it along a path that grows a controlled, fairly even amount with each pull, and a careful person can keep the tear more or less where they want it for a surprisingly long distance, resisting the pull in a way that still feels like ordinary paper. Then, once enough of the sheet's width has been torn through, the same steady pull suddenly rips the remaining strip apart in one fast motion that offers almost no resistance at all, the change from controlled tearing to sudden separation arriving with no real warning beyond the fact that less paper was left to hold onto. A fatigue crack behaves the same way for essentially the same reason: what is left of the intact material has to carry the whole of the applied load, and as that remaining material shrinks it eventually reaches a point where it simply cannot, and everything past that point happens far faster than anything before it.
Why the crack tip gets more dangerous as it grows
The reason the growth accelerates rather than staying steady all the way to the end comes down to what a growing crack does to the stress right at its own leading edge. A sharp crack concentrates stress at its tip the same way any sharp notch does, and the sharper and longer the crack becomes, the more severely that tip concentrates the stress passing through the surrounding material, so a crack that has already grown some distance is sitting in a locally more stressed environment than the same crack was earlier in its life, purely because of its own length. This creates a feedback loop rather than a fixed rate: a longer crack drives a higher local stress at its tip, and a higher local stress drives faster growth on the next cycle, so the growth rate itself keeps climbing even while the externally applied load never changes. Once the crack reaches a length where the remaining material's strength is finally overwhelmed by that locally amplified stress, the slow, cycle-by-cycle growth of the first phase gives way to the near-instantaneous tearing of the second, and a part that had been quietly shedding a little more of its remaining margin with every single load cycle finally runs out of margin altogether. Nothing about the load itself needs to change for this to happen, which is the detail that makes the failure feel unprovoked when it arrives, since the part can be doing exactly the same job it did the day before, at exactly the same force, and simply be carrying a crack that has, on its own, crossed the line between slow and fast.
The number that matters here
The final, unstable phase of a fatigue crack's growth can consume the last several millimetres of a part's remaining cross-section in a fraction of a second, even though reaching that same crack length by the slow, stable route beforehand may have taken years of ordinary repeated use, so the two phases of one continuous crack can differ in speed by many orders of magnitude despite belonging to the identical failure.
What this changes in practice
Because the great majority of a fatigue crack's total life is spent in the slow, stable phase, a part that is inspected often enough relative to how quickly its cracks grow has a genuine window in which a crack can be found and the part retired or repaired before anything dramatic happens, and this is the entire logic behind scheduled inspection of fatigue-prone structures rather than simply running parts until they fail. The number that has to be got right is not whether a crack exists, since almost any part that has carried enough repeated load eventually will have one, but how much stable growth remains before that crack crosses into its unstable phase, because once it does, the remaining warning time shrinks from years to essentially nothing. A crack detected early, while it is still growing slowly, is a maintenance problem with options attached to it: a part can be repaired, reinforced locally, or retired on a schedule that gives whoever depends on it time to plan around the loss. A crack detected in its final phase, if it is detected at all before the part simply lets go, has already run out of the slow warning that made early detection possible in the first place, which is exactly why the inspection interval itself has to be set against how fast a crack of the smallest reliably detectable size can grow, rather than against how the part has behaved so far, since past behaviour describes only the slow phase and says nothing about how close any given crack already sits to the fast one.