I don't have a properties of materials text in front of my so I can't answer quantitatively, but I can tell you qualitatively what happens. The primary principals of the strength of materials start with beam theory. This calculates how much load you can put on a structural element like a building beam. It is based on a smooth distribution of stresses across the area of any cross-section you would cut through your beam. Basically the bigger the cross-section (actually the bigger the moment of inertia of the cross-section), the stronger the beam is at that point.
Beam theory sort of ignores the size and shape of the cross-section next to the one you're examining. The cross-sections work independently like links in a chain. Under stress the weak link may break, but a funny distribution of link shapes in the neighborhood won't have much effect on your weak link.
Beam theory was found woefully lacking when they started to build iron ships. They discovered that ships would break in half starting at the corners of square hatches in the decks. The ships were strong enough based on beam theory, but broke anyway. This did not happen with wooden ships.
It turns out that hard materials often can't stretch enough to smoothly distribute their stresses under tension. The big problem comes in areas where the cross-section of the material changes suddenly. If you cut a notch in the side of a hardened steel bolt stresses concentrate (rise) at the bottom of the notch. The stress in the bolt under simple tension is not even across the smallest cross-section of the bolt, they may be 10 times higher right at the base of the notch. You might not notice this with a mild steel bolt, but you do with hardened steel. (And that isn't as hard as a knife blade). To really see the problem, see what a notch from a diamond can do to weaken glass.
You can get stress rise at sharp sholders, notches, holes, etc. It is worst at the surface. It is worst when it is a sharp 'V' shape. It is least with smooth curves.
Weirdest of all, you can sometimes reduce stress rising by drilling a small hole through a material a short distance under a notch. That redistributes the stresses and makes them "flow" more smoothly. More importantly it reduces stresses right at the base of the notch.
[This message has been edited by Jeff Clark (edited 11-25-2000).]
