Fillets are not decoration

Why internal corners get a radius, and what it does to the stress there.

An internal corner cut sharp, with no radius at all, becomes the exact point where stress concentration is most severe under load, because force flowing through a part has to change direction there just as suddenly as the corner itself does, and a fillet exists to give that force a gentler path to follow, spreading the same load across a wider area rather than letting it pile up in one infinitely thin line.

Why a crease tears and a curve survives

Folding a sheet of paper sharply along one line and then flexing it back and forth concentrates all of that bending into the single thin crease, and the paper tears along exactly that line after only a few flexes, because the strain has nowhere else to go. Bending the same sheet into a gentle curve, with no crease anywhere, spreads the bending across a wide arc of paper, and it survives far longer, because no single point is being asked to absorb all the strain by itself. A sharp internal corner on a loaded part behaves like the crease, and a fillet like the gentle curve. Nobody who wants paper to survive flexing creases it on purpose, and a designer adding a fillet is acting on the same instinct before the part is ever loaded.

How force bends its way around a corner

Force travelling through a loaded part follows paths that bend and spread out to avoid a sharp change in direction wherever the shape allows it, in much the same way water flowing through a bend prefers a wide sweeping curve over a sudden turn. At a sharp internal corner the part's geometry forces those paths to turn suddenly and tightly at one point, and because more of the load is squeezed through a smaller region there than anywhere nearby, the local stress at the corner rises far above the average stress in the rest of the part. A fillet, a small radius added where two surfaces would otherwise meet in a sharp line, gives the force a gentler curve to follow, spreading the same load over a wider region and lowering the peak. Nothing else in the part changes, only the shape of that one corner, and yet the whole part becomes stronger because its weakest point no longer gathers load the way it did.

The size of the effect is easiest to see in the simplest case. Even a perfectly round hole drilled in a wide plate that is being pulled triples the stress at the edge of the hole, compared with the stress in the plate well away from it. A sharp corner is worse than a round hole, and in the idealised limit of a corner with no radius at all, the calculated peak stress has no upper limit. Real materials yield a little and blunt the corner before that happens, but the lesson holds, and it is why a crack, when a part eventually fails, so often starts at an unfilleted internal corner.

Small radii, routinely applied

Because the benefit comes mostly from removing the sudden direction change itself, even a small fillet, one that barely alters the part's shape or appearance, captures most of the reduction in peak stress. A radius of a fraction of the wall thickness is usually enough, which is why fillets are added as a matter of routine at every internal corner on a loaded part, and not only at places that look as though they need extra strength. A drawing with one internal corner left sharp where the surrounding ones were carefully filleted is worth a second look, since that corner is rarely a deliberate choice and far more often the one nobody noticed. A crack starting at exactly that corner, on a part where every other corner survived, is about the clearest evidence there is that the fillets elsewhere were doing structural work.