Pull on a steel plate and the force travels through it along invisible lines, spread evenly like traffic on a wide motorway. Cut a hole in the plate and the lines in its way have to go round. They squeeze through the metal beside the hole, and where they bunch up the metal carries far more load per square millimetre than anywhere else. Nothing is wrong with the metal. The hole just left less of it in the way.
Engineers compare the peak stress at a hole with the average stress in the plate far away. The ratio is called the stress concentration factor, written Kt. For a round hole in a large plate pulled in one direction, Kt is 3: at the two points of the hole at right angles to the pull, the metal feels three times the stress you would guess from the pull alone.
In 1913 the engineer Charles Inglis worked out the answer for an elliptical hole: Kt = 1 + 2a/b. Here a is the half-width of the hole across the pull and b is its half-height along the pull. A circle has a = b, so Kt = 3. Make the hole a wide, flat slit across the pull and the 2a/b term keeps growing.
The same formula can be written 1 + 2√(a/ρ), where ρ is the radius of the curve at the tip of the hole. A tighter curve means a higher peak. That is the whole story of sharp corners: a corner is a curve with a tiny radius, so the force lines cannot turn without crowding together. In theory, the stress at a perfectly sharp corner has no upper limit. In practice the metal yields or cracks instead.
The plate below is pulled up and down. Drag the lime handles to stretch the hole sideways or up and down, or use a preset. Watch the force lines crowd at the tips and the factor change.
The Kt number is exact for an ellipse in a very large plate (Inglis). The force lines are a sketch of the flow, not a calculation.
Two things to try. Stretch the hole up and down, along the pull, and Kt falls towards 1: a slot lined up with the force lines barely disturbs them. Then make it wide and flat and Kt shoots past 10. The shape of the tip matters more than the size of the hole.
A single pull at three times the average stress is usually survivable. An aircraft cabin is different. It is pressurised on every flight and relaxed on landing, so the skin is stretched and released again and again. Metal loaded and unloaded thousands of times can grow a crack even when every single load is far below what would break it in one go. This is fatigue, and cracks start where the stress is highest. The peak, not the average, decides how long the part lasts.
The de Havilland Comet was the first jet airliner. On 10 January 1954 a BOAC Comet broke up in the air near the island of Elba, killing all 35 people aboard. On 8 April 1954 a South African Airways Comet broke up near Naples, killing all 21. Investigators at the Royal Aircraft Establishment put another Comet fuselage into a giant water tank and pressurised it over and over. That fuselage had already flown 1,230 pressurised flights. It failed after another 1,830 simulated ones, with a crack starting at the corner of a squarish escape-hatch window.
The wreckage from Elba showed the same kind of failure. The first fracture was traced to the squarish roof windows for the radio direction finder, and the metal carried the unmistakable marks of fatigue. That aircraft had made 1,290 pressurised flights. The Naples aircraft, with 900, left too little wreckage for a firm conclusion, but nothing found contradicted the Elba finding. Cracks also grew from rivet holes near the windows, which add their own stress peaks to the corners. Later Comets were built with oval windows.
Round the corners, and make the radius generous. Turn slots so that their long side lies along the load. Add extra metal around an opening, so there is more material to share the crowded force. And when a crack has already started, drill a small round hole at its tip. The tip of a crack is as sharp as a curve can be; a drilled hole replaces it with a smooth edge, where the stress is still high but no longer without limit.
The next time you look out of an airliner window, notice the shape: the rounded corners are not for looks. Every curve on it is a place where a crack would otherwise have a head start.