The bracket that passed the calculation and failed anyway

A part checked for stress and never checked for the thing that broke it.

A bracket can pass a stress calculation with a comfortable margin and still fail in service, because a static calculation only checks whether the part survives one worst-case peak load. It says nothing about what happens after that part has been loaded and unloaded thousands of times, which is the condition almost every bracket on a moving vehicle actually lives in.

Damage that adds up one cycle at a time

A static stress calculation asks whether the highest load the part will ever see stays safely below the load at which the material would yield or break. Fatigue asks a different question: how many times that load, or something like it, has been applied and removed. Every cycle, even one far below the part's static strength, does a tiny amount of damage, usually starting at a small imperfection such as a sharp corner, a scratch or a tool mark. That damage accumulates until a crack has grown large enough to finish the part off suddenly, often at a load the same part shrugged off easily the first time.

Bending a paperclip back and forth shows this precisely. The first bend takes deliberate effort and the clip survives it undamaged. Keep bending at the same spot and the wire eventually snaps in two at a bend that felt no harder than any before it, because each bend added a little damage where the previous ones had already weakened the wire. Stop halfway and inspect the clip, and there is usually nothing to see, since the damage at that stage is far too small for the naked eye.

The number of cycles a part survives falls steeply as the load rises. For many steels there is a stress, typically around half the material's tensile strength when measured on a polished test bar, below which the part will survive an effectively unlimited number of cycles. A bracket loaded a little above that line can crack within weeks of vibration, while one loaded comfortably below it can outlive the vehicle.

Checking for cycles and looking at corners

A part loaded only once or twice in its life can reasonably be checked with a single static calculation. A part loaded repeatedly, which covers almost any bracket on a vehicle that moves, also needs checking against a fatigue limit, a lower figure than its static strength, and lower still on a real part with a rough surface and a sharp corner than on a polished test bar.

Fatigue cracks overwhelmingly start at stress concentrations: sharp internal corners, small holes, and sudden changes in section thickness. A bracket that looks perfectly adequate under a smooth static load can still carry a local hot spot that a crack will find and grow from long before the part's overall strength is threatened. A generous fillet radius on an inside corner, or a hole moved slightly away from a highly loaded edge, costs almost nothing in material or machining time, yet it can multiply the life of the part, which is why these small details get so much attention on anything that sees repeated loading.

My key error with this

I sized that bracket against the largest load I expected it to see, confirmed it had a comfortable margin against yield, and considered the analysis finished, which it would have been if the load had only ever arrived once. The bracket was carrying a sensor on a car, so the load arrived several times a second for the whole of every session, and it eventually broke through fatigue at a stress that my static calculation had been entirely happy with. Losing the sensor cost considerably more than the bracket did, and it cost more than I could comfortably absorb at that point. What replaced the belief is that a static check answers a question about one event and says nothing about a million of them, and that anything mounted to a vibrating structure needs its life read off a curve of stress against cycles rather than compared against a single strength figure. That curve has been one of the two charts I reach for most often ever since, second only to the one that decides which material I should have been holding in the first place.