stress concentration

Try to tear a sheet of paper straight across — it is surprisingly hard. Now make a tiny nick at the edge first, and it tears easily right there. The nick did not weaken the whole sheet; it concentrated all the pulling right at its tip. Stress concentration is this everyday fact: any hole, notch, sharp corner, or scratch locally multiplies the stress far above the average you calculated from force divided by area.

The applied stress lines (think of them flowing like water) have to bend around a flaw and crowd together at its tip, so the local stress there is higher. For a small circular hole in a wide plate the peak is three times the average stress. For a sharper flaw it is worse: the stress-concentration factor Kt for an elliptical hole is about Kt = 1 + 2 times sqrt(a/rho), where a is the flaw's half-length and rho is the radius at its tip. A long, sharp crack (tiny rho) makes Kt huge — which is why sharp corners are dangerous and rounded fillets are safe.

This is why real parts are far weaker than a smooth test bar, and why designers round off corners, add generous fillets, and polish out scratches. It also explains the gap between theoretical strength (from breaking every atomic bond at once) and actual strength (a crack tip breaks bonds one row at a time). A ductile metal can blunt a stress raiser by yielding locally; a brittle material cannot, so for ceramics and glass stress raisers are deadly.