Why a small hole can cause a big problem — and why the exact same notch is a footnote in one material and a fatigue crack's origin in another.
Drill a hole through the middle of a loaded plate and the average stress across what's left of the cross-section barely changes — a little less area is carrying the same force, so σ = F/A ticks up modestly. But the stress right at the edge of that hole is nowhere near the average. It spikes to several times the nominal value, because the load lines that used to pass straight through now have to crowd around the obstacle, piling up right at its edge. That local spike is a stress concentration, and it is the single most common starting point for real-world cracks and fractures — not the thick, heavily-loaded section of a part, but the small geometric detail everyone assumed was harmless.