For the techies: A stress concentrator is a geometric feature which distorts the stress field in a sheet of material .
In the real world, however, it means that any hole, especially a narrow, pointy hole a-- 'crack'-- in a sheet of material has a disproportionate effect on the local stress near the hole. That effect can be enough to make the whole sheet of metal break into two pieces.
And what that means is that a crack--even if it is visible only in a microscope-- can raise the local stresses by a factor of 10, 100 or even 1000. If the material is stressed in the first place, such a stress concentration can result in a crack which grows very quickly, leading to a complete fracture of the metal sheet.
The most famous example of a crack leading to wholesale structural failure is the Liberty ships built quickly and at low-cost during the 1939-45 war. The hulls were made of all-welded steel plates, instead of riveted plates. The welds were, in many cases, created by unskilled workers. As such, they contained tiny cracks, which became stress concentrators. When the ships sailed in Arctic waters, the cold temperatures made the thin, low-grade steel relatively brittle. Brittle steel, combined with microscopic cracks in the welds led to large cracks in the steel. Because the hulls were welded as one continuous piece of steel, the cracks propagated all the way through the hull, leading the ships to break, literally, in half.
These failures led to the science of fracture mechanics, and by the end of the war, the failure rate in these ships had fallen from 30 percent to under 5 percent, thanks to improved design and better welding practices.
What happens is that the amount of stress concentrated in the tip of the crack depends not on the size of the crack, but on the ratio of length to width. A round hole, such as a porthole, or rivet hole doubles the stress around itself, irrespective of diameter. On the other hand, the type of crack formed in a bad weld might be only 1mm long, but with a very sharp tip. This long, thin shape makes the local stress at the crack tip many hundreds of times the local average stress levels.
What happens then depends on many things, but in the worst case, there is enough energy at the crack tip to create two new surfaces, and that means the crack propagates—it grows. If there is nothing to stop the crack growing, it will keep opening up until the whole piece of metal has broken.
Worst case means that the metal is brittle (not ductile) which means the atomic lattice is fairly rigid and not forgiving of small movements. A ductile material requires far more energy to create a new surface than a brittle material (think how easy it is to smash glass, and how hard to smash a sheet of copper). So it is hard to make a crack grow in a ductile material.
Since then, fracture mechanics has become a very well-researched area, and people now know a whole lot more about the science of cracks and crack growth. Nowadays, it is less of an issue in ships than in aircraft or other safety-critical systems. On news reports you will sometimes here reports that an aircraft had cracks in the tailplane, or some such. The engineers are less worried about the size of the crack than their shape. This is why they will be just as worried about microscopic cracks as large, visible ones.
The stress concentration factor, K is the stress at the crack tip (σt) divided by the bulk stress in the material (σ0) This is calculated from the formula:
K = σt/σ0 = 2(a/rt)^0.5
where a is the crack depth (or half the crack length if the crack is in the body of the material)
and rt is the radius of the crack at the crack tip